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The Asymptotic Efficiency of Conditional Likelihood Methods

Kung-Yee Liang
Biometrika
Vol. 71, No. 2 (Aug., 1984), pp. 305-313
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336247
Stable URL: http://www.jstor.org/stable/2336247
Page Count: 9
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The Asymptotic Efficiency of Conditional Likelihood Methods
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Abstract

This paper concerns the efficiency of the conditional likelihood method for inference in models which include nuisance parameters. A new concept of ancillarity, asymptotic weak ancillarity, is introduced. It is shown that the conditional maximum likelihood estimator and the conditional score test of θ, the parameter of interest, are asymptotically equivalent to their unconditional counterparts, and hence are asymptotically efficient, provided that the conditioning statistic is asymptotically weakly ancillary. The key assumption that the conditioning statistic is asymptotically weakly ancillary is verified when the underlying distribution is from exponential families. Some illustrative examples are given.

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