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B1516
Topic: Contributions on likelihood Title: Distribution of likelihood-based $p-$values under the alternative hypothesis Authors:  Alastair Young - Imperial College London (United Kingdom) [presenting]
Stephen Lee - The University of Hong Kong (Hong Kong)
Abstract: We consider inference on a scalar interest parameter in the presence of a nuisance parameter, using a likelihood-based statistic which is asymptotically normally distributed under the null hypothesis. Higher-order expansions are used to compare the repeated sampling distribution, under a general contiguous alternative hypothesis, of $p-$values calculated from the asymptotic normal approximation to the null sampling distribution of the statistic with those calculated by bootstrap approximations. Comparisons of different testing procedures in terms of power under an alternative hypothesis are closely related to differences under the null hypothesis, specifically the extent to which testing procedures are conservative or anti-conservative under the null. Empirical examples are presented which demonstrate that higher-order asymptotic effects may be clearly seen in small sample contexts.