Prof. Alastair Young (Imperial College) Sampling Distributions of Likelihood-based p-values
samedi 02 jui 2016
Elvezio Ronchetti 60th birthday workshop
1Opening
14:38
2Prof. Anna-Clara Monti (Università degli Studi del Sannio)55:07
3Prof. Roy Welsch (MIT)48:40
4Prof. Alastair Young (Imperial College) 01:02:13
5Prof. Yanyuan Ma (University of South Carolina)49:45
6Prof. Alan Welsh (Australian National University)01:01:19
7Prof. Loriano Mancini (Swiss Federal Institute of Technology)56:20
8Closing11:26
We consider the problem of inference for 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. Two approaches to calculation of an approximate p-value are: analytic methods
based on normal approximation to an adjusted form of statistic; simulation (`bootstrap')
approximation to the null sampling distribution of the statistic. Higher-order expansions are used to
compare the sampling distributions, under a general contiguous alternative hypothesis, of p-values
calculated by these different approaches. We establish that comparisons in terms of power under an
alternative hypothesis are intrinsically linked to the extent to which testing procedures are
conservative or anti-conservative under the null. Empirical examples are discussed which
demonstrate that higher-order asymptotic effects may be clearly seen in small sample contexts.
This is joint work with Stephen Lee (University of Hong Kong).