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Dümbgen, Lutz; Walther, Günther

Multiscale inference about a density. (English) Zbl 1142.62336

Ann. Stat. 36, No. 4, 1758-1785 (2008).
Summary: 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.

Cited in 1 Review
Cited in 41 Documents

MSC:

62G07 Density estimation
62G10 Nonparametric hypothesis testing
62G15 Nonparametric tolerance and confidence regions
62G30 Order statistics; empirical distribution functions
62G20 Asymptotic properties of nonparametric inference
62N03 Testing in survival analysis and censored data
65C60 Computational problems in statistics (MSC2010)

Keywords:

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

Software:

ftnonpar; SiZer
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Full Text: DOI arXiv

References:

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