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New Goodness-of-Fit Tests and their Application toNonparametric Confidence Sets

Dümbgen, Lutz

In: The Annals of Statistics, 26 (1998), Nr. 1. pp. 288-314. ISSN 0090-5364

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Abstract

Suppose one observes a process V on the unit interval, wheredV(t) = f(t) + dW(t) with an unknown function f and standard Brownian motion W. We propose a particular test of one-point hypotheses about f which is based on suitably standardized increments of V.This test is shown to have desirable consistency properties if, for instance, fis restricted to various Hölder smoothness classes of functions. Thetest is mimicked in the context of nonparametric density estimation,nonparametric regression and interval censored data. Under shaperestrictions on the parameter f such as monotonicity or convexity, weobtain confidence sets for f adapting to its unknown smoothness.

Item Type: Article
Journal or Publication Title: The Annals of Statistics
Volume: 26
Number: 1
Publisher: IMS Business Office
Place of Publication: Hayward, Calif.
Date Deposited: 09 Jun 2016 07:52
Date: 1998
ISSN: 0090-5364
Page Range: pp. 288-314
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 310 General statistics
510 Mathematics
Uncontrolled Keywords: Adaptivity; conditional median; convexity; distribution-free; interval censoring; modality; monotonicity; signs of residuals; spacings
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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