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Multiscale inference about a density
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DOI：10.1214/07-AOS521.png)
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Abstract
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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.
Keywords:
exponential inequality
modes
monotone failure rate
multiple test
order statistics
spacings
subexponential increments
sub-Gaussian tails
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