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|a (JST)4616851
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|a eng
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|a Romano, Joseph P.
|e verfasserin
|4 aut
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|a On Non-Parametric Testing, the Uniform Behaviour of the t-Test, and Related Problems
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|c 2004
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|a Text
|b txt
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|a In this article, we revisit some problems in non-parametric hypothesis testing. First, we extend the classical result of Bahadur & Savage [Ann. Math. Statist. 25 (1956) 1115] to other testing problems, and we answer a conjecture of theirs. Other examples considered are testing whether or not the mean is rational, testing goodness-of-fit, and equivalence testing. Next, we discuss the uniform behaviour of the classical t-test. For most non-parametric models, the Bahadur-Savage result yields that the size of the t-test is one for every sample size. Even if we restrict attention to the family of symmetric distributions supported on a fixed compact set, the t-test is not even uniformly asymptotically level α. However, the convergence of the rejection probability is established uniformly over a large family with a very weak uniform integrability type of condition. Furthermore, under such a restriction, the t-test possesses an asymptotic maximin optimality property.
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|a Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics
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|a asymptotically maximin
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|a confidence intervals
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|a hypothesis tests
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|a large sample theory
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|a Philosophy
|x Applied philosophy
|x Philosophy of science
|x Scientific method
|x Hypothesis testing
|x T tests
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|a Philosophy
|x Applied philosophy
|x Philosophy of science
|x Scientific method
|x Hypothesis testing
|x Null hypothesis
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Random variables
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|a Mathematics
|x Pure mathematics
|x Probability theory
|x Probabilities
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Statistical results
|x Statistical properties
|x Estimate reliability
|x Confidence interval
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|a Mathematics
|x Applied mathematics
|x Statistics
|x Applied statistics
|x Descriptive statistics
|x Statistical distributions
|x Distribution functions
|x Probability distributions
|x Mathematical moments
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|a Mathematics
|x Applied mathematics
|x Game theory
|x Maximin
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|a Mathematics
|x Pure mathematics
|x Geometry
|x Euclidean geometry
|x Geometric lines
|x Real lines
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|a Mathematics
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|a Philosophy
|x Applied philosophy
|x Philosophy of science
|x Scientific method
|x Hypothesis testing
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|a research-article
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|i Enthalten in
|t Scandinavian Journal of Statistics
|d Blackwell Publishers, 1974
|g 31(2004), 4, Seite 567-584
|w (DE-627)266018297
|w (DE-600)1466951-1
|x 14679469
|7 nnns
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|g volume:31
|g year:2004
|g number:4
|g pages:567-584
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|u https://www.jstor.org/stable/4616851
|3 Volltext
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|d 31
|j 2004
|e 4
|h 567-584
|