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

The limit distribution of weighted $$L^2$$ L 2 -goodness-of-fit statistics under fixed... 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 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of the Institute of Statistical Mathematics Springer Journals

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

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Publisher
Springer Japan
Copyright
Copyright © 2016 by The Institute of Statistical Mathematics, Tokyo
Subject
Statistics; Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance
ISSN
0020-3157
eISSN
1572-9052
D.O.I.
10.1007/s10463-016-0567-8
Publisher site
See Article on Publisher Site

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 .

Journal

Annals of the Institute of Statistical MathematicsSpringer Journals

Published: Jun 14, 2016

References

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