In: The Annals of Statistics, 26 (1998), Nr. 1. S. 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.
Dokumententyp: | Artikel |
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Titel der Zeitschrift: | The Annals of Statistics |
Band: | 26 |
Nummer: | 1 |
Verlag: | IMS Business Office |
Ort der Veröffentlichung: | Hayward, Calif. |
Erstellungsdatum: | 09 Jun. 2016 07:52 |
Erscheinungsjahr: | 1998 |
ISSN: | 0090-5364 |
Seitenbereich: | S. 288-314 |
Institute/Einrichtungen: | Fakultät für Mathematik und Informatik > Institut für Mathematik |
DDC-Sachgruppe: | 310 Statistik
510 Mathematik |
Freie Schlagwörter: | Adaptivity; conditional median; convexity; distribution-free; interval censoring; modality; monotonicity; signs of residuals; spacings |
Schriftenreihe: | Beiträge zur Statistik > Beiträge |