Efficiency of projected score methods in rectangular array asymptotics
Haihong Li, Bruce G. Lindsay, Richard P. Waterman
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2003 · Volume 65 · Issue 1
Abstract
Summary.The paper considers a rectangular array asymptotic embedding for multistratum data sets, in which both the number of strata and the number of within-stratum replications increase, and at the same rate. It is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non-zero mean in its asymptotic normal distribution. By using a projection operator on the score function, an adjusted maximum likelihood estimator can be obtained that is asymptotically unbiased and has a variance that attains the Cramér–Rao lower bound. The adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator.
Keywords
Asymptotic theory, Neyman–Scott problem, Nuisance parameters, Projected score, Rectangular array
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