M. Rosenblatt :
“Remarks on higher order spectra ,”
pp. 383–389
in
Multivariate analysis
(Dayton, OH, 14–19 February 1965 ).
Edited by P. R. Krishnaiah .
Academic Press (New York ),
1966 .
MR
211568
Zbl
0213.19601
incollection
People
BibTeX
@incollection {key211568m,
AUTHOR = {Rosenblatt, Murray},
TITLE = {Remarks on higher order spectra},
BOOKTITLE = {Multivariate analysis},
EDITOR = {Krishnaiah, Paruchuri R.},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1966},
PAGES = {383--389},
NOTE = {(Dayton, OH, 14--19 February 1965).
MR:211568. Zbl:0213.19601.},
}
M. Rosenblatt :
“Conditional probability density and regression estimators ,”
pp. 25–31
in
Multivariate analysis, II
(Dayton, OH, 17–22 June 1968 ).
Edited by P. R. Krishnaiah .
Academic Press (New York ),
1969 .
MR
254987
incollection
People
BibTeX
@incollection {key254987m,
AUTHOR = {Rosenblatt, M.},
TITLE = {Conditional probability density and
regression estimators},
BOOKTITLE = {Multivariate analysis, {II}},
EDITOR = {Krishnaiah, Paruchuri R.},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1969},
PAGES = {25--31},
NOTE = {(Dayton, OH, 17--22 June 1968). MR:254987.},
}
P. Bickel and M. Rosenblatt :
“Two-dimensional random fields ,”
pp. 3–15
in
Multivariate analysis, III
(Dayton, OH, 19–24 June 1972 ).
Edited by P. R. Krishnaiah .
Academic Press (New York ),
1973 .
MR
348832
Zbl
0297.60020
incollection
People
BibTeX
@incollection {key348832m,
AUTHOR = {Bickel, P. and Rosenblatt, M.},
TITLE = {Two-dimensional random fields},
BOOKTITLE = {Multivariate analysis, {III}},
EDITOR = {Krishnaiah, Paruchuri R.},
PUBLISHER = {Academic Press},
ADDRESS = {New York},
YEAR = {1973},
PAGES = {3--15},
DOI = {10.1016/B978-0-12-426653-7.50006-5},
NOTE = {(Dayton, OH, 19--24 June 1972). MR:348832.
Zbl:0297.60020.},
ISBN = {9780124266537},
}
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).},
}
P. A. W. Lewis, L. H. Liu, D. W. Robinson, and M. Rosenblatt :
“Empirical sampling study of a goodness of fit statistic for density function estimation ,”
pp. 159–174
in
Multivariate analysis IV
(Dayton, OH, 16–21 June 1975 ).
Edited by P. R. Krishnaiah .
1977 .
Zbl
0399.62039
incollection
Abstract
People
BibTeX
The distribution of a measure of the distance between a probability density function and its estimate is examined through empirical sampling methods. The estimate of the density function is that proposed by Rosenblatt using sums of weight functions centered at the observed values of the random variables. The weight function in all cases was triangular, but both uniform and Cauchy densities were tried for different sample sizes and bandwidths. The simulated distributions look as if they could be approximated by Gamma distributions, in many cases. Some assessment can also be made of the rate of convergence of the moments and the distribution of the measure to the limiting moments and distribution, respectively.
@incollection {key0399.62039z,
AUTHOR = {Lewis, P. A. W. and Liu, L. H. and Robinson,
D. W. and Rosenblatt, M.},
TITLE = {Empirical sampling study of a goodness
of fit statistic for density function
estimation},
BOOKTITLE = {Multivariate analysis {IV}},
EDITOR = {Krishnaiah, Paruchuri R.},
YEAR = {1977},
PAGES = {159--174},
URL = {https://apps.dtic.mil/dtic/tr/fulltext/u2/a012465.pdf},
NOTE = {(Dayton, OH, 16--21 June 1975). Zbl:0399.62039.},
ISBN = {9780720405200},
}
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},
}
M. Rosenblatt :
“Some limit theorems for partial sums of stationary sequences ,”
pp. 239–248
in
Multivariate analysis, V
(Amsterdam ).
Edited by P. R. Krishnaiah .
North-Holland ,
1980 .
MR
566342
Zbl
0422.60018
incollection
People
BibTeX
@incollection {key566342m,
AUTHOR = {Rosenblatt, M.},
TITLE = {Some limit theorems for partial sums
of stationary sequences},
BOOKTITLE = {Multivariate analysis, {V}},
EDITOR = {Krishnaiah, Paruchuri Rama},
PUBLISHER = {North-Holland},
YEAR = {1980},
PAGES = {239--248},
NOTE = {(Amsterdam). MR:566342. Zbl:0422.60018.},
ISBN = {9780444853219},
}
J. Rice and M. Rosenblatt :
“Boundary effects on the behavior of smoothing splines ,”
pp. 635–643
in
Statistics and probability: Essays in honor of C. R. Rao .
Edited by G. Kallianpur, P. R. Krishnaiah, and J. K. Ghosh .
North-Holland (Amsterdam ),
1982 .
MR
659512
Zbl
0524.41008
incollection
People
BibTeX
@incollection {key659512m,
AUTHOR = {Rice, J. and Rosenblatt, M.},
TITLE = {Boundary effects on the behavior of
smoothing splines},
BOOKTITLE = {Statistics and probability: {E}ssays
in honor of {C}.~{R}. {R}ao},
EDITOR = {Kallianpur, Gopinath and Krishnaiah,
Paruchuri R. and Ghosh, J. K.},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1982},
PAGES = {635--643},
NOTE = {MR:659512. Zbl:0524.41008.},
ISBN = {9780444861306},
}
M. Rosenblatt :
“Cumulants and cumulant spectra ,”
pp. 369–382
in
Time series in the frequency domain .
Edited by D. R. Brillinger and P. R. Krishnaiah .
Handbook of Statistics 3 .
North-Holland (Amsterdam ),
1983 .
MR
749794
Zbl
0539.93071
incollection
People
BibTeX
@incollection {key749794m,
AUTHOR = {Rosenblatt, M.},
TITLE = {Cumulants and cumulant spectra},
BOOKTITLE = {Time series in the frequency domain},
EDITOR = {Brillinger, D. R. and Krishnaiah, P.
R.},
SERIES = {Handbook of Statistics},
NUMBER = {3},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1983},
PAGES = {369--382},
DOI = {10.1016/S0169-7161(83)03019-9},
NOTE = {MR:749794. Zbl:0539.93071.},
ISSN = {0169-7161},
ISBN = {9780444867261},
}
K. S. Lii and M. Rosenblatt :
“A fourth-order deconvolution technique for non-Gaussian linear processes ,”
pp. 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 :
“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},
}