Local efficiency of integrated goodness-of-fit tests under skew alternatives

@article{ADurio2016LocalEO,
  title={Local efficiency of integrated goodness-of-fit tests under skew alternatives},
  author={A.Durio and Ya. Yu. Nikitin},
  journal={arXiv: Statistics Theory},
  year={2016}
}
The efficiency of distribution-free {\it integrated} goodness-of-fit tests was studied by Henze and Nikitin (2000, 2002) under location alternatives. We calculate local Bahadur efficiencies of these tests under more realistic generalized skew alternatives. They turn out to be unexpectedly high. 

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References

SHOWING 1-10 OF 25 REFERENCES
Local Bahadur efficiency of some goodness-of-fit tests under skew alternatives
Abstract The efficiency of most known distribution-free goodness-of-fit tests such as Kolmogorov–Smirnov, Cramer–von Mises and their variants was studied mainly under the classical alternatives ofExpand
A new approach to goodness-of-fit testing based on the integrated empirical process
This paper takes a new approach to goodness-of-fit testing, based on Kolmogorov-Smirnov and Cramér-von Mises type functionals of the suitably integrated empirical process. A key limiting process isExpand
New two-sample tests based on the integrated empirical copula processes
We introduce a new test of equality between two dependence structures. The new statistics are functionals of a suitably integrated two-sample empirical copula process. The limiting behaviours of theExpand
Testing the Equality of Multivariate Distributions Using the Bootstrap and Integrated Empirical Processes
We introduce some projected integrated empirical processes for testing the equality of two multivariate distributions. The bootstrap is used for determining the approximate critical values. We showExpand
Anderson-Darling Type Goodness-of-t Statistic Based on a Multifold Integrated Empirical Distribution Function
An Anderson-Darling type goodness-of-fit statistic constructed from multifold integrated empirical distribution function is proposed. The proposed statistic is of an integral form whose integrand isExpand
Empirical Processes with Applications to Statistics
Here is the first book to summarize a broad cross-section of the large volume of literature available on one-dimensional empirical processes. Presented is a thorough treatment of the theory ofExpand
Asymptotic Efficiency of Nonparametric Tests: Contents
Some asymptotic results for the integrated empirical process with applications to statistical tests
ABSTRACT The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence ofExpand
The Skew-Normal and Related Families
TLDR
This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers, and Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques. Expand
Some Limit Theorems in Statistics
Moment-generating Functions Chernoff's Theorem The Kullback- Leibler Information Number Some Examples of Large Deviation Probabilities Stein's Lemma Asymptotic Effective Variances Exact Slopes ofExpand
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