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November, 1973 On Some Global Measures of the Deviations of Density Function Estimates
P. J. Bickel, M. Rosenblatt
Ann. Statist. 1(6): 1071-1095 (November, 1973). DOI: 10.1214/aos/1176342558


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.


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P. J. Bickel. M. Rosenblatt. "On Some Global Measures of the Deviations of Density Function Estimates." Ann. Statist. 1 (6) 1071 - 1095, November, 1973.


Published: November, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0275.62033
MathSciNet: MR348906
Digital Object Identifier: 10.1214/aos/1176342558

Keywords: asymptotic distribution , bandwidth , density function estimates , functionals of stochastic process , Gaussian process , global measure of deviation , ‎weight function

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 6 • November, 1973
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