Celebratio Mathematica — Rosenblatt

Murray Rosenblatt
1926–2019

Works connected to Peter J. Bickel

Filter the Bibliography List

year	title	people

			clear

P. J. Bickel and M. Rosenblatt: “On some global measures of the deviations of density function estimates,” Ann. Stat. 1 : 6 (1973), pp. 1071–1095. Corrections to this article were published in Ann. Stat. 3:6 (1975). MR 348906 Zbl 0275.62033 article

We consider density estimates of the usual type generated by a weight function. Limt theorems are obtained for the maximum of the normalized deviation of the estimate from its expected value, and for quadratic norms of the same quantity. Using these results we study the behavior of tests of goodness-of-fit and confidence regions based on these statistics. In particular, we obtain a procedure which uniformly improves the chi-square goodness-of-fit test when the number of observations and cells is large and yet remains insensitive to the estimation of nuisance parameters. A new limit theorem for the maximum absolute value of a type of nonstationary Gaussian process is also proved.

Murray Rosenblatt1926–2019

Works connected to Peter J. Bickel

Filter the Bibliography List

Murray Rosenblatt
1926–2019