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.
Document type: | Article |
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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 > Institut für Mathematik |
DDC-classification: | 310 General statistics 510 Mathematics |
Uncontrolled Keywords: | Adaptivity; conditional median; convexity; distribution-free; interval censoring; modality; monotonicity; signs of residuals; spacings |
Series: | Beiträge zur Statistik > Beiträge |