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Likelihood Ratio Tests with Ranks

Michael Woodroofe
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 46, No. 2 (Jun., 1984), pp. 233-252
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25050482
Page Count: 20
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Likelihood Ratio Tests with Ranks
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Abstract

Let $X_{1},..,X_{m}$ and $Y_{1},..,Y_{n}$ be independent random samples from distributions F and G and consider the problem of testing $H_{0}$: F = G against the alternative that Y is either stochastically larger than X or stochastically smaller, using the ranks of the combined sample. The submodel $G={\rm F}^{\theta}$ for some unknown θ, 0 < θ < ∞ is used to generate a likelihood function from which a maximum likelihood estimate of θ and a likelihood ratio statistic may be computed Asymptotic distributions and large deviations rates are obtained for these statistics and Bahadur efficiencies of the rank likelihood ratio test with respect to natural competitors are computed. The rank likelihood ratio test may be used to perform repeated significance tests of $H_{0}$ over time. Properties of the sequential procedure are determined.

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