K. S. Lii, M. Rosenblatt, and C. Van Atta :
“Bispectral measurements in turbulence, I J. Fluid Mech.
77 : 1
(September 1975 ),
pp. 45–62 .
article
Abstract
People
BibTeX
@article {key32451786,
AUTHOR = {Lii, K. S. and Rosenblatt, M. and Van
Atta, C.},
TITLE = {Bispectral measurements in turbulence,
{I}},
JOURNAL = {J. Fluid Mech.},
FJOURNAL = {Journal of Fluid Mechanics},
VOLUME = {77},
NUMBER = {1},
MONTH = {September},
YEAR = {1975},
PAGES = {45--62},
DOI = {10.1017/S0022112076001122},
ISSN = {0022-1120},
}
K.-S. Lii and M. Rosenblatt :
“Asymptotic results on a spline estimate of a probability density 77–85
in
Statistical inference and related topics
(Bloomington, IN, 31 July–9 August 1974 ),
vol. 2 .
Edited by M. L. Puri .
Academic Press (New York ),
1975 .
Volume dedicated to Z. W. Birnbaum.
MR
373139 Zbl
0341.62033 incollection
People
BibTeX
@incollection {key373139m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Asymptotic results on a spline estimate
of a probability density},
BOOKTITLE = {Statistical inference and related topics},
EDITOR = {Puri, Madan Lal},
VOLUME = {2},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1975},
PAGES = {77--85},
DOI = {10.1016/B978-0-12-568002-8.50010-0},
NOTE = {(Bloomington, IN, 31 July--9 August
1974). Volume dedicated to Z.~W. Birnbaum.
MR:373139. Zbl:0341.62033.},
ISBN = {9780125680028},
}
K. S. Lii and M. Rosenblatt :
“Asymptotic behavior of a spline estimate of a density function Comput. Math. Appl.
1 : 2
(June 1975 ),
pp. 223–235 .
MR
386134 Zbl
0364.62037 article
Abstract
People
BibTeX
@article {key386134m,
AUTHOR = {Lii, Keh Shin and Rosenblatt, M.},
TITLE = {Asymptotic behavior of a spline estimate
of a density function},
JOURNAL = {Comput. Math. Appl.},
FJOURNAL = {Computers \& Mathematics with Applications},
VOLUME = {1},
NUMBER = {2},
MONTH = {June},
YEAR = {1975},
PAGES = {223--235},
DOI = {10.1016/0898-1221(75)90021-8},
NOTE = {MR:386134. Zbl:0364.62037.},
ISSN = {0898-1221},
}
K. N. Helland, K. S. Lii, and M. Rosenblatt :
“Bispectra of atmospheric and wind tunnel turbulence ,”
pp. 223–248
in
Application of Statistics
(Dayton, OH, 14–20 June 1976 ).
Edited by P. R. Krishnaiah .
North-Holland (Amsterdam ),
1977 .
incollection
People
BibTeX
@incollection {key74274431,
AUTHOR = {Helland, K. N. and Lii, K. S. and Rosenblatt,
M.},
TITLE = {Bispectra of atmospheric and wind tunnel
turbulence},
BOOKTITLE = {Application of Statistics},
EDITOR = {Krishnaiah, P. R.},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1977},
PAGES = {223--248},
NOTE = {(Dayton, OH, 14--20 June 1976).},
}
K. N. Helland, K. S. Lii, and M. Rosenblatt :
“Bispectra and energy transfer in grid-generated turbulence Chapter 3 ,
pp. 123–155
in
Developments in statistics ,
vol. 2 .
Edited by P. R. Krishnaiah .
Developments in statistics .
Academic Press (New York ),
1979 .
MR
554179 Zbl
0478.76060 incollection
People
BibTeX
@incollection {key554179m,
AUTHOR = {Helland, K. N. and Lii, K. S. and Rosenblatt,
M.},
TITLE = {Bispectra and energy transfer in grid-generated
turbulence},
BOOKTITLE = {Developments in statistics},
EDITOR = {Krishnaiah, Paruchuri R.},
CHAPTER = {3},
VOLUME = {2},
SERIES = {Developments in statistics},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1979},
PAGES = {123--155},
DOI = {10.1016/B978-0-12-426602-5.50009-8},
NOTE = {MR:554179. Zbl:0478.76060.},
ISSN = {0163-3384},
ISBN = {9780124266025},
}
K. S. Lii, K. N. Helland, and M. Rosenblatt :
“Estimating three-dimensional energy transfer in isotropic turbulence J. Time Ser. Anal.
3 : 1
(1982 ),
pp. 1–28 .
MR
660393 Zbl
0501.76044 article
Abstract
People
BibTeX
In order to obtain an estimate of three-dimensional energy transfer in grid-generated turbulence, second and third order spectra are statistically estimated. A Monte Carlo Fourier transformation of bispectra is carried out so as to gauge energy transfer between wavenumber shells.
@article {key660393m,
AUTHOR = {Lii, K. S. and Helland, K. N. and Rosenblatt,
M.},
TITLE = {Estimating three-dimensional energy
transfer in isotropic turbulence},
JOURNAL = {J. Time Ser. Anal.},
FJOURNAL = {Journal of Time Series Analysis},
VOLUME = {3},
NUMBER = {1},
YEAR = {1982},
PAGES = {1--28},
DOI = {10.1111/j.1467-9892.1982.tb00327.x},
NOTE = {MR:660393. Zbl:0501.76044.},
ISSN = {0143-9782},
}
K. S. Lii and M. Rosenblatt :
“Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes Ann. Stat.
10 : 4
(1982 ),
pp. 1195–1208 .
MR
673654 Zbl
0512.62090 article
Abstract
People
BibTeX
@article {key673654m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {Deconvolution and estimation of transfer
function phase and coefficients for
non-{G}aussian linear processes},
JOURNAL = {Ann. Stat.},
FJOURNAL = {Annals of Statistics},
VOLUME = {10},
NUMBER = {4},
YEAR = {1982},
PAGES = {1195--1208},
DOI = {10.1214/aos/1176345984},
NOTE = {MR:673654. Zbl:0512.62090.},
ISSN = {0090-5364},
}
K. S. Lii and M. Rosenblatt :
“Remarks on non-Gaussian linear processes with additive Gaussian noise 185–197
in
Robust and nonlinear time series analysis
(Heidelberg, September 1983 ).
Lecture Notes in Statistics 26 .
Springer (New York ),
1984 .
MR
786308 Zbl
0568.62078 incollection
People
BibTeX
@incollection {key786308m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {Remarks on non-{G}aussian linear processes
with additive {G}aussian noise},
BOOKTITLE = {Robust and nonlinear time series analysis},
SERIES = {Lecture Notes in Statistics},
NUMBER = {26},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {1984},
PAGES = {185--197},
DOI = {10.1007/978-1-4615-7821-5_10},
NOTE = {(Heidelberg, September 1983). MR:786308.
Zbl:0568.62078.},
ISSN = {0930-0325},
ISBN = {9781461578215},
}
K. S. Lii and M. Rosenblatt :
“Non-Gaussian linear processes, phase and deconvolution ,”
pp. 51–58
in
Statistical signal processing
(Annapolis, MD, 11–15 May 1982 ).
Edited by E. J. Wegman and J. G. Smith .
Statistics: Textbooks and Monographs 53 .
Marcel Dekker (New York ),
1984 .
MR
787247 Zbl
0563.62067 incollection
People
BibTeX
@incollection {key787247m,
AUTHOR = {Lii, Keh Shin and Rosenblatt, Murray},
TITLE = {Non-{G}aussian linear processes, phase
and deconvolution},
BOOKTITLE = {Statistical signal processing},
EDITOR = {Wegman, Edward J. and Smith, James G.},
SERIES = {Statistics: Textbooks and Monographs},
NUMBER = {53},
PUBLISHER = {Marcel Dekker},
ADDRESS = {New York},
YEAR = {1984},
PAGES = {51--58},
NOTE = {(Annapolis, MD, 11--15 May 1982). MR:787247.
Zbl:0563.62067.},
ISSN = {0039-0550},
ISBN = {9780824771591},
}
K. S. Lii and M. Rosenblatt :
“A fourth-order deconvolution technique for non-Gaussian linear processes 395–410
in
Multivariate analysis VI
(Pittsburgh, PA, 25–29 July 1983 ).
Edited by P. R. Krishnaiah .
North-Holland (Amsterdam ),
1985 .
MR
822309 Zbl
0587.60035 incollection
Abstract
People
BibTeX
In Lii and Rosenblatt [1982] a deconvolution scheme for non-Gaussian linear processes making use of third order momnets (or spectra) was presented. This is appropriate for such processes with nonzero third order central moments. However, if the third order moments are zero (this could happen in the case of symmetric distributions) it is appropriate to look for a fourth order technique that would be effective. Such a scheme is presented and discussed in this paper together with more illustrative examples.
@incollection {key822309m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {A fourth-order deconvolution technique
for non-{G}aussian linear processes},
BOOKTITLE = {Multivariate analysis {VI}},
EDITOR = {Krishnaiah, Paruchuri R.},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1985},
PAGES = {395--410},
URL = {https://apps.dtic.mil/dtic/tr/fulltext/u2/a120663.pdf},
NOTE = {(Pittsburgh, PA, 25--29 July 1983).
MR:822309. Zbl:0587.60035.},
ISBN = {9780444876027},
}
K.-S. Lii and M. Rosenblatt :
“Deconvolution of non-Gaussian linear processes with vanishing spectral values Proc. Natl. Acad. Sci. U.S.A.
83 : 2
(February 1986 ),
pp. 199–200 .
MR
822711 Zbl
0582.60052 article
Abstract
People
BibTeX
@article {key822711m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Deconvolution of non-{G}aussian linear
processes with vanishing spectral values},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {83},
NUMBER = {2},
MONTH = {February},
YEAR = {1986},
PAGES = {199--200},
DOI = {10.1073/pnas.83.2.199},
NOTE = {MR:822711. Zbl:0582.60052.},
ISSN = {0027-8424},
}
K. S. Lii and M. Rosenblatt :
“Estimation of a transfer function in a non-Gaussian context 49–51
in
Function estimates
(Arcata, CA, 28 July–3 August 1985 ).
Edited by J. S. Marron .
Contemporary Mathematics 59 .
American Mathematical Society (Providence, RI ),
1986 .
MR
870447 Zbl
0646.62077 incollection
People
BibTeX
@incollection {key870447m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {Estimation of a transfer function in
a non-{G}aussian context},
BOOKTITLE = {Function estimates},
EDITOR = {Marron, J. S.},
SERIES = {Contemporary Mathematics},
NUMBER = {59},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1986},
PAGES = {49--51},
DOI = {10.1090/conm/059/870447},
NOTE = {(Arcata, CA, 28 July--3 August 1985).
MR:870447. Zbl:0646.62077.},
ISSN = {0271-4132},
ISBN = {9780821850626},
}
K.-S. Lii and M. Rosenblatt :
“Estimation and deconvolution when the transfer function has zeros J. Theoret. Probab.
1 : 1
(1988 ),
pp. 93–113 .
MR
916486 Zbl
0668.62071 article
Abstract
People
BibTeX
The problem of estimation of the transfer function and deconvolution of a linear process is considered. This paper specifically deals with the case when the transfer function has zeros on the unit circle or equivalently the spectral density function has zeros. It is shown that if the zeros are finitely many and are of finite order then we can still consistently estimate the transfer function without the minimum phase assumption when the process is non-Gaussian. Statistical properties of the estimate are given. Convergence of the deconvolution is also given. It is shown that if the transfer function vanishes on an interval, then, essentially, we cannot identify the transfer function. Two simple simulated examples are given to illustrate the procedures.
@article {key916486m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Estimation and deconvolution when the
transfer function has zeros},
JOURNAL = {J. Theoret. Probab.},
FJOURNAL = {Journal of Theoretical Probability},
VOLUME = {1},
NUMBER = {1},
YEAR = {1988},
PAGES = {93--113},
DOI = {10.1007/BF01076289},
NOTE = {MR:916486. Zbl:0668.62071.},
ISSN = {0894-9840},
}
K.-S. Lii and M. Rosenblatt :
“Nonminimum phase non-Gaussian deconvolution J. Multivar. Anal.
27 : 2
(November 1988 ),
pp. 359–374 .
Republished in a 1989 print book version of this volume .
MR
970960 Zbl
0658.60069 article
Abstract
People
BibTeX
@article {key970960m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Nonminimum phase non-{G}aussian deconvolution},
JOURNAL = {J. Multivar. Anal.},
FJOURNAL = {Journal of Multivariate Analysis},
VOLUME = {27},
NUMBER = {2},
MONTH = {November},
YEAR = {1988},
PAGES = {359--374},
DOI = {10.1016/0047-259X(88)90135-2},
NOTE = {Republished in a 1989 print book version
of this volume. MR:970960. Zbl:0658.60069.},
ISSN = {0047-259X},
}
K.-S. Lii and M. Rosenblatt :
“Nonminimum phase non-Gaussian deconvolution ,”
pp. 359–374
in
Multivariate statistics and probability: Essays in memory of Paruchuri R. Krishnaiah .
Edited by C. R. Rao .
1989 .
Republished from J. Multivar. Anal. 27 :2 (1988)
Zbl
0697.62089 incollection
Abstract
People
BibTeX
@incollection {key0697.62089z,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Nonminimum phase non-{G}aussian deconvolution},
BOOKTITLE = {Multivariate statistics and probability:
{E}ssays in memory of {P}aruchuri {R}.
{K}rishnaiah},
EDITOR = {Rao, C. R.},
YEAR = {1989},
PAGES = {359--374},
NOTE = {Republished from \textit{J. Multivar.
Anal.} \textbf{27}:2 (1988). Zbl:0697.62089.},
ISBN = {9780125802055},
}
F. J. Breidt, R. A. Davis, K.-S. Lii, and M. Rosenblatt :
“Nonminimum phase non-Gaussian autoregressive processes Proc. Natl. Acad. Sci. U.S.A.
87 : 1
(1990 ),
pp. 179–181 .
MR
1031950 Zbl
0686.62068 article
Abstract
People
BibTeX
The structure of non-Gaussian autoregressive schemes is described. Asymptotically efficient methods for the estimation of the coefficients of the models are described under appropriate conditions, some of which relate to smoothness and positivity of the density function \( f \) of the independent random variables generating the process. The principal interest is in nonminimum phase models.
@article {key1031950m,
AUTHOR = {Breidt, F. Jay and Davis, Richard A.
and Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Nonminimum phase non-{G}aussian autoregressive
processes},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {87},
NUMBER = {1},
YEAR = {1990},
PAGES = {179--181},
DOI = {10.1073/pnas.87.1.179},
NOTE = {MR:1031950. Zbl:0686.62068.},
ISSN = {0027-8424},
}
K. S. Lii and M. Rosenblatt :
“Asymptotic normality of cumulant spectral estimates J. Theor. Probab.
3 : 2
(April 1990 ),
pp. 367–385 .
MR
1046340 Zbl
0716.62094 article
Abstract
People
BibTeX
@article {key1046340m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {Asymptotic normality of cumulant spectral
estimates},
JOURNAL = {J. Theor. Probab.},
FJOURNAL = {Journal of Theoretical Probability},
VOLUME = {3},
NUMBER = {2},
MONTH = {April},
YEAR = {1990},
PAGES = {367--385},
DOI = {10.1007/BF01045168},
NOTE = {MR:1046340. Zbl:0716.62094.},
ISSN = {0894-9840},
}
K. S. Lii and M. Rosenblatt :
“Cumulant spectral estimates: Bias and covariance ,”
pp. 365–405
in
Limit theorems in probability and statistics
(Pécs, Hungary, 3–7 July 1989 ).
Edited by I. Berkes, E. Csáki, and P. Révész .
Colloquia Mathematica Societatis János Bolyai 57 .
North-Holland (Amsterdam ),
1990 .
MR
1116799 Zbl
0727.62090 incollection
People
BibTeX
@incollection {key1116799m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {Cumulant spectral estimates: {B}ias
and covariance},
BOOKTITLE = {Limit theorems in probability and statistics},
EDITOR = {Berkes, I. and Cs\'aki, E. and R\'ev\'esz,
P.},
SERIES = {Colloquia Mathematica Societatis J\'anos
Bolyai},
NUMBER = {57},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1990},
PAGES = {365--405},
NOTE = {(P\'ecs, Hungary, 3--7 July 1989). MR:1116799.
Zbl:0727.62090.},
ISSN = {0139-3383},
ISBN = {9780444987587},
}
F. J. Breidt, R. A. Davis, K.-S. Lii, and M. Rosenblatt :
“Maximum likelihood estimation for noncausal autoregressive processes J. Multivar. Anal.
36 : 2
(February 1991 ),
pp. 175–198 .
MR
1096665 Zbl
0711.62072 article
Abstract
People
BibTeX
We discuss a maximum likelihood procedure for estimating parameters in possibly noncausal autoregressive processes driven by i.i.d. non-Gaussian noise. Under appropriate conditions, estimates of the parameters that are solutions to the likelihood equations exist and are asymptotically normal. The estimation procedure is illustrated with a simulation study for \( \mathrm{AR}(2) \) processes.
@article {key1096665m,
AUTHOR = {Breidt, F. Jay and Davis, Richard A.
and Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Maximum likelihood estimation for noncausal
autoregressive processes},
JOURNAL = {J. Multivar. Anal.},
FJOURNAL = {Journal of Multivariate Analysis},
VOLUME = {36},
NUMBER = {2},
MONTH = {February},
YEAR = {1991},
PAGES = {175--198},
DOI = {10.1016/0047-259X(91)90056-8},
NOTE = {MR:1096665. Zbl:0711.62072.},
ISSN = {0047-259X},
}
K. Helland, K. S. Lii, and M. Rosenblatt :
“Monte Carlo and turbulence 405–418
in
Nonparametric functional estimation and related topics
(Spetses, Greece, 29 July–10 August 1990 ).
Edited by G. Roussas .
NATO ASI Series. Series C. Mathematics and Physical Sciences 335 .
Kluwer Academic (Dordrecht, The Netherlands ),
1991 .
MR
1154342 Zbl
0737.76035 incollection
Abstract
People
BibTeX
In a prior paper an estimate of three-dimensional energy transfer was attempted in grid-generated turbulence by using estimates of second and third order spectra and employing Monte Carlo estimates of integrals. The methods used in such a Monte Carlo simulation are considered in greater detail. To see how well such a technique using Monte Carlo works, a smaller problem involving second order spectra with the results known analytically is employed. Some general remarks are also made on Monte Carlo estimates of Fourier transforms.
@incollection {key1154342m,
AUTHOR = {Helland, K. and Lii, K. S. and Rosenblatt,
M.},
TITLE = {Monte {C}arlo and turbulence},
BOOKTITLE = {Nonparametric functional estimation
and related topics},
EDITOR = {Roussas, George},
SERIES = {NATO ASI Series. Series C. Mathematics
and Physical Sciences},
NUMBER = {335},
PUBLISHER = {Kluwer Academic},
ADDRESS = {Dordrecht, The Netherlands},
YEAR = {1991},
PAGES = {405--418},
DOI = {10.1007/978-94-011-3222-0_31},
NOTE = {(Spetses, Greece, 29 July--10 August
1990). MR:1154342. Zbl:0737.76035.},
ISSN = {0258-2023},
ISBN = {9780792312260},
}
K.-S. Lii and M. Rosenblatt :
“An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes J. Multivar. Anal.
43 : 2
(November 1992 ),
pp. 272–299 .
MR
1193615 Zbl
0765.62082 article
Abstract
People
BibTeX
An approximate maximum likelihood procedure is proposed for the estimation of parameters in possibly nonminimum phase (noninvertible) moving average processes driven by independent and identically distributed non-Gaussian noise. Under appropriate conditions, parameter estimates that are solutions of likelihood-like equations are consistent and are asymptotically normal. A simulation study for \( \mathrm{MA}(2) \) processes illustrates the estimation procedure.
@article {key1193615m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {An approximate maximum likelihood estimation
for non-{G}aussian non-minimum phase
moving average processes},
JOURNAL = {J. Multivar. Anal.},
FJOURNAL = {Journal of Multivariate Analysis},
VOLUME = {43},
NUMBER = {2},
MONTH = {November},
YEAR = {1992},
PAGES = {272--299},
DOI = {10.1016/0047-259X(92)90037-G},
NOTE = {MR:1193615. Zbl:0765.62082.},
ISSN = {0047-259X},
}
K.-S. Lii and M. Rosenblatt :
“Bispectra and phase of non-Gaussian linear processes J. Theor. Probab.
6 : 3
(1993 ),
pp. 579–593 .
MR
1230347 Zbl
0774.62089 article
Abstract
People
BibTeX
The phase of the transfer function of linear processes which cannot be identified in the Gaussian case can be almost fully resolved in the non-Gaussian case. Estimates have been proposed in the past. A nonparametric estimate of the phase with better asymptotic convergence properties as a function of sample size is studied here. The asymptotic behavior of the bias and variance of the estimate is examined. In particular the variance of the phase estimate is shown to be asymptotically independent of the frequency (if the frequency is not zero). Related problems are of interest in deconvolution, transfer function estimation, as well as in the resolution of astronomical images (perturbed by atmospheric turbulence) obtained by earth based telescopes.
@article {key1230347m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Bispectra and phase of non-{G}aussian
linear processes},
JOURNAL = {J. Theor. Probab.},
FJOURNAL = {Journal of Theoretical Probability},
VOLUME = {6},
NUMBER = {3},
YEAR = {1993},
PAGES = {579--593},
DOI = {10.1007/BF01066718},
NOTE = {MR:1230347. Zbl:0774.62089.},
ISSN = {0894-9840},
}
K.-S. Lii and M. Rosenblatt :
“Non-Gaussian autoregressive moving average processes Proc. Natl. Acad. Sci. U.S.A.
90 : 19
(October 1993 ),
pp. 9168–9170 .
MR
1246981 Zbl
0779.62076 article
Abstract
People
BibTeX
Non-Gaussian stationary autoregressive moving average sequences are considered. Under conditions concerning smoothness and positivity of the density function of the independent random variables generating the sequence, asymptotically efficient methods for the estimation of unknown coefficients of the model are described. The main interest is in nonminimum-phase models.
@article {key1246981m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Non-{G}aussian autoregressive moving
average processes},
JOURNAL = {Proc. Natl. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {90},
NUMBER = {19},
MONTH = {October},
YEAR = {1993},
PAGES = {9168--9170},
DOI = {10.1073/pnas.90.19.9168},
NOTE = {MR:1246981. Zbl:0779.62076.},
ISSN = {0027-8424},
}
K.-S. Lii and M. Rosenblatt :
“Maximum likelihood estimation for non-Gaussian nonminimum phase ARMA sequences Statist. Sinica
6 : 1
(1996 ),
pp. 1–22 .
MR
1379046 Zbl
0839.62085 article
Abstract
People
BibTeX
We consider an approximate maximum likelihood procedure for estimating
parameters of possibly noncausal and noninvertible autoregressive moving average
processes driven by independent identically distributed non-Gaussian noise. It is shown
that the normalized approximate likelihood has a global maximum at true parameter
values in the non-Gaussian case. Under appropriate conditions, estimates of parameters that are solutions of likelihood equations exist, are consistent and asymptotically normal. An asymptotic covariance matrix is given. The procedure is illustrated with simulation examples of \( \mathrm{ARMA}(1,1) \) processes.
@article {key1379046m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Maximum likelihood estimation for non-{G}aussian
nonminimum phase {ARMA} sequences},
JOURNAL = {Statist. Sinica},
FJOURNAL = {Statistica Sinica},
VOLUME = {6},
NUMBER = {1},
YEAR = {1996},
PAGES = {1--22},
URL = {https://www.jstor.org/stable/24305996},
NOTE = {MR:1379046. Zbl:0839.62085.},
ISSN = {1017-0405},
}
K.-S. Lii and M. Rosenblatt :
“Nongaussian autoregressive sequences and random fields 295–309
in
Stochastic modelling in physical oceanography .
Edited by R. J. Adler, P. Müller, and B. Rozovskii .
Progress in Probability 39 .
Birkhäuser (Boston ),
1996 .
MR
1383877 Zbl
0865.76075 incollection
Abstract
People
BibTeX
In this paper we discuss estimation procedures for the parameters of autoregressive schemes. There is a large literature concerned with estimation in the one-dimensional Gaussian case. Much of our discussion will however be dedicated to the non-Gaussian context, some aspects of which have been considered only in recent years. Results have also at times been obtained in the broader context of autoregressive moving average schemes. We restrict ourselves to the case of autoregressive schemes for the sake of simplicity. Also they are the discrete analogue of simple versions of stochastic differential equations with constant coefficients. It is also apparent that non-Gaussian autoregressive stationary sequences have a richer and more complicated structure than that of the Gaussian autoregressive stationary sequences.
@incollection {key1383877m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Nongaussian autoregressive sequences
and random fields},
BOOKTITLE = {Stochastic modelling in physical oceanography},
EDITOR = {Adler, Robert J. and M\"uller, Peter
and Rozovskii, Boris},
SERIES = {Progress in Probability},
NUMBER = {39},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston},
YEAR = {1996},
PAGES = {295--309},
DOI = {10.1007/978-1-4612-2430-3_11},
NOTE = {MR:1383877. Zbl:0865.76075.},
ISSN = {1050-6977},
ISBN = {9781461224303},
}
K.-S. Lii and M. Rosenblatt :
“Line spectral analysis for harmonizable processes Proc. Natl. Acad. Sci. USA
95 : 9
(1998 ),
pp. 4800–4803 .
MR
1619284 Zbl
0899.62118 article
Abstract
People
BibTeX
@article {key1619284m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Line spectral analysis for harmonizable
processes},
JOURNAL = {Proc. Natl. Acad. Sci. USA},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {95},
NUMBER = {9},
YEAR = {1998},
PAGES = {4800--4803},
DOI = {10.1073/pnas.95.9.4800},
NOTE = {MR:1619284. Zbl:0899.62118.},
ISSN = {0027-8424},
}
K.-S. Lii and M. Rosenblatt :
“Spectral analysis for harmonizable processes Ann. Stat.
30 : 1
(2002 ),
pp. 258–297 .
A correction to this article ws published in Ann. Stat. 31 :5 (2003)
MR
1892664 Zbl
1012.62099 article
Abstract
People
BibTeX
Spectral estimation of nonstationary but harmonizable processes is considered. Given a single realization of the process, periodogram-like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines. Such a process can arise in signals of a moving source from array data or multipath signals with Doppler stretch from a single receiver. Such processes also include periodically correlated (or cyclostationary) and almost periodically correlated processes as special cases. We give detailed analysis on aliasing, bias and covariances of various estimators. It is shown that dividing a single long realization of the process into nonoverlapping subsections and then averaging periodogram-like estimates formed from each subsection will not yield meaningful results if one is estimating spectral mass with support on lines with slope not equal to 1. If the slope of a spectral support line is irrational, then spectral masses do not fold on top of each other in estimation even if the data are equally spaced. Simulation examples are given to illustrate various theoretical results.
@article {key1892664m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Spectral analysis for harmonizable processes},
JOURNAL = {Ann. Stat.},
FJOURNAL = {Annals of Statistics},
VOLUME = {30},
NUMBER = {1},
YEAR = {2002},
PAGES = {258--297},
DOI = {10.1214/aos/1015362193},
NOTE = {A correction to this article ws published
in \textit{Ann. Stat.} \textbf{31}:5
(2003). MR:1892664. Zbl:1012.62099.},
ISSN = {0090-5364},
}
K.-S. Lii and M. Rosenblatt :
“Correction: ‘Spectral analysis for harmonizable processes’ Ann. Stat.
31 : 5
(2003 ),
pp. 1693 .
Correction to an article published in Ann. Stat. 30 :1 (2002)
MR
2012830 article
People
BibTeX
@article {key2012830m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Correction: ``{S}pectral analysis for
harmonizable processes''},
JOURNAL = {Ann. Stat.},
FJOURNAL = {Annals of Statistics},
VOLUME = {31},
NUMBER = {5},
YEAR = {2003},
PAGES = {1693},
DOI = {10.1214/aos/1065705123},
NOTE = {Correction to an article published in
\textit{Ann. Stat.} \textbf{30}:1 (2002).
MR:2012830.},
ISSN = {0090-5364},
}
K.-S. Lii and M. Rosenblatt :
“Estimation for almost periodic processes Ann. Stat.
34 : 3
(2006 ),
pp. 1115–1139 .
A correction to this article was published in Ann. Stat. 36 :3 (2008)
MR
2278353 Zbl
1113.62111 article
Abstract
People
BibTeX
@article {key2278353m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Estimation for almost periodic processes},
JOURNAL = {Ann. Stat.},
FJOURNAL = {Annals of Statistics},
VOLUME = {34},
NUMBER = {3},
YEAR = {2006},
PAGES = {1115--1139},
DOI = {10.1214/009053606000000218},
NOTE = {A correction to this article was published
in \textit{Ann. Stat.} \textbf{36}:3
(2008). MR:2278353. Zbl:1113.62111.},
ISSN = {0090-5364},
}
K.-S. Lii and M. Rosenblatt :
“Correction: ‘Estimation for almost periodic processes’ Ann. Stat.
36 : 3
(2008 ),
pp. 1508 .
Correction to an article published in Ann. Stat. 34 :3 (2006)
MR
2418665 article
People
BibTeX
@article {key2418665m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Correction: ``{E}stimation for almost
periodic processes''},
JOURNAL = {Ann. Stat.},
FJOURNAL = {Annals of Statistics},
VOLUME = {36},
NUMBER = {3},
YEAR = {2008},
PAGES = {1508},
DOI = {10.1214/07-AOS502},
NOTE = {Correction to an article published in
\textit{Ann. Stat.} \textbf{34}:3 (2006).
MR:2418665.},
ISSN = {0090-5364},
}
K. S. Lii and M. Rosenblatt :
“Prolate spheroidal spectral estimates Statist. Probab. Lett.
78 : 11
(August 2008 ),
pp. 1339–1348 .
MR
2444324 Zbl
1144.62079 article
Abstract
People
BibTeX
An estimate of the spectral density of a stationary time series can be obtained by taking the finite Fourier transform of an observed sequence \( x_0 \) , \( x_1,\dots \) , \( x_{N-1} \) of sample size \( N \) with taper a discrete prolate spheroidal sequence and computing its square modulus. It is typical to take the average \( K \) of several such estimates corresponding to different prolate spheroidal sequences with the same bandwidth \( W(N) \) as the final computed estimate. For the mean square error of such an estimate to converge to zero as \( N\to\infty \) , it is shown that it is necessary to have \( W(N)\downarrow 0 \) with
\[ NW(N)\to\infty \]
as \( N\to\infty \) and significantly have
\[ K(N) \leq 2NW(N) \]
but \( K = K(N)\to\infty \) as \( N\to\infty \) .
@article {key2444324m,
AUTHOR = {Lii, K. S. and Rosenblatt, M.},
TITLE = {Prolate spheroidal spectral estimates},
JOURNAL = {Statist. Probab. Lett.},
FJOURNAL = {Statistics \& Probability Letters},
VOLUME = {78},
NUMBER = {11},
MONTH = {August},
YEAR = {2008},
PAGES = {1339--1348},
DOI = {10.1016/j.spl.2008.05.022},
NOTE = {MR:2444324. Zbl:1144.62079.},
ISSN = {0167-7152},
}
M. Rosenblatt :
Selected works of Murray Rosenblatt R. A. Davis, K.-S. Lii, and D. N. Politis .
Selected Works in Probability and Statistics .
Springer (Berlin ),
2011 .
MR
2742596 Zbl
1232.60004 book
People
BibTeX
@book {key2742596m,
AUTHOR = {Rosenblatt, Murray},
TITLE = {Selected works of {M}urray {R}osenblatt},
SERIES = {Selected Works in Probability and Statistics},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2011},
PAGES = {xxxvi+1348},
DOI = {10.1007/978-1-4419-8339-8},
NOTE = {Edited by R. A. Davis,
K.-S. Lii, and D. N. Politis.
MR:2742596. Zbl:1232.60004.},
ISBN = {9781441983381},
}
K.-S. Lii and M. Rosenblatt :
“Estimation for a class of nonstationary processes Statist. Probab. Lett.
81 : 11
(November 2011 ),
pp. 1612–1622 .
MR
2832920 Zbl
1227.62077 article
Abstract
People
BibTeX
Random processes with almost periodic covariance function are considered from a spectral outlook. Given suitable conditions, spectral estimation problems are discussed for Gaussian processes of this type that are neither stationary nor locally stationary. Spectral mass is concentrated on lines parallel to the main diagonal in the spectral plane. A method of estimation of the support of spectral mass under appropriate restraints is considered. Some open questions are discussed. Extension of the methods for a class of non-Gaussian nonstationary processes with mean value function a trigonometric regression is given. Consistent estimates for frequency, amplitude and phase of the regression are noted when the residual process is zero mean almost periodic. The resulting estimation of the spectral mass of the residual is also considered.
@article {key2832920m,
AUTHOR = {Lii, Keh-Shin and Rosenblatt, Murray},
TITLE = {Estimation for a class of nonstationary
processes},
JOURNAL = {Statist. Probab. Lett.},
FJOURNAL = {Statistics \& Probability Letters},
VOLUME = {81},
NUMBER = {11},
MONTH = {November},
YEAR = {2011},
PAGES = {1612--1622},
DOI = {10.1016/j.spl.2011.06.009},
NOTE = {MR:2832920. Zbl:1227.62077.},
ISSN = {0167-7152},
}
