The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed alternatives, with applications

L. Baringhaus (), B. Ebner () and N. Henze ()
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L. Baringhaus: Leibniz Universität Hannover
B. Ebner: Institut für Stochastik
N. Henze: Institut für Stochastik

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 5, No 2, 969-995

Abstract: Abstract We present a general result on the limit distribution of weighted one- and two-sample $$L^2$$ L 2 -goodness-of-fit test statistics of some hypothesis $$H_0$$ H 0 under fixed alternatives. Applications include an approximation of the power function of such tests, asymptotic confidence intervals of the distance of an underlying distribution with respect to the distributions under $$H_0$$ H 0 , and an asymptotic equivalence test that is able to validate certain neighborhoods of $$H_0$$ H 0 .

Keywords: Goodness-of-fit test; Weighted $$L^2$$ L 2 -statistic; Fixed alternative; Empirical transform; Asymptotic equivalence test (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (19)

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DOI: 10.1007/s10463-016-0567-8

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