The Annals of Statistics

Multiscale inference about a density

Lutz Dümbgen and Günther Walther

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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

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

First available in Project Euclid: 16 July 2008

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Zentralblatt MATH identifier

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

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


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

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