Intermediate efficiency by shifting alternatives and evaluation of power

We study a modification of the notion of asymptotic intermediate efficiency of statistical tests by defining it in terms of shifting alternatives. We prove a theorem providing conditions for its existence and show that this modification is closely related to the original Kallenberg's asymptotic...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2010-11, Vol.140 (11), p.3263-3281
Main Author: Inglot, Tadeusz
Format: Article
Language:English
Subjects:
Anderson–Darling test
Asymptotic intermediate efficiency
Chi-square test
Cramér–von Mises test
Evaluation of power
Exact sciences and technology
General topics
Goodness of fit
Kolmogorov–Smirnov test
Mathematics
Multivariate analysis
Neyman–Pearson test
Parametric inference
Probability and statistics
Sampling theory, sample surveys
Sciences and techniques of general use
Shifted alternatives
Statistics
Vanishing shortcoming
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Summary:We study a modification of the notion of asymptotic intermediate efficiency of statistical tests by defining it in terms of shifting alternatives. We prove a theorem providing conditions for its existence and show that this modification is closely related to the original Kallenberg's asymptotic intermediate efficiency in a quite general setting. Next, we find estimates for differences between powers of the Neyman–Pearson test under original alternatives and that of a given test under shifted alternatives. We also present some simulation results. They attest to consistency of theoretical results with observed empirical powers for quite small sample sizes.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.04.019