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February 1998 New goodness-of-fit tests and their application to nonparametric confidence sets
Lutz Dümbgen
Ann. Statist. 26(1): 288-314 (February 1998). DOI: 10.1214/aos/1030563987

Abstract

Suppose one observes a process V on the unit interval, where $dV = f_o + dW$ with an unknown parameter $f_o \epsilon L_1[0, 1]$ and standard Brownian motion W. We propose a particular test of one-point hypotheses about $f_o$ which is based on suitably standardized increments of V. This test is shown to have desirable consistency properties if, for instance, $f_o$ is restricted to various Hölder classes of functions. The test is mimicked in the context of nonparametric density estimation, nonparametric regression and interval-censored data. Under shape restrictions on the parameter, such as monotonicity or convexity, we obtain confidence sets for $f_o$ adapting to its unknown smoothness.

Citation

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Lutz Dümbgen. "New goodness-of-fit tests and their application to nonparametric confidence sets." Ann. Statist. 26 (1) 288 - 314, February 1998. https://doi.org/10.1214/aos/1030563987

Information

Published: February 1998
First available in Project Euclid: 28 August 2002

zbMATH: 0930.62034
MathSciNet: MR1611768
Digital Object Identifier: 10.1214/aos/1030563987

Subjects:
Primary: 62G07, 62G15

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 1 • February 1998
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