The Annals of Statistics

Multiscale inference about a density

Lutz Dümbgen and Günther Walther

Full-text: Open access

Abstract

We introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate. The procedure provides guaranteed finite-sample significance levels, is easy to implement and possesses certain asymptotic optimality and adaptivity properties.

Article information

Source
Ann. Statist., Volume 36, Number 4 (2008), 1758-1785.

Dates
First available in Project Euclid: 16 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1216237299

Digital Object Identifier
doi:10.1214/07-AOS521

Mathematical Reviews number (MathSciNet)
MR2435455

Zentralblatt MATH identifier
1142.62336

Subjects
Primary: 62G07: Density estimation 62G10: Hypothesis testing 62G15: Tolerance and confidence regions 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions

Keywords
Exponential inequality modes monotone failure rate multiple test order statistics spacings subexponential increments sub-Gaussian tails

Citation

Dümbgen, Lutz; Walther, Günther. Multiscale inference about a density. Ann. Statist. 36 (2008), no. 4, 1758--1785. doi:10.1214/07-AOS521. https://projecteuclid.org/euclid.aos/1216237299


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