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Efficiency of projected score methods in rectangular array asymptotics

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  • Haihong Li
  • Bruce G. Lindsay
  • Richard P. Waterman

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.

Suggested Citation

  • Haihong Li & Bruce G. Lindsay & Richard P. Waterman, 2003. "Efficiency of projected score methods in rectangular array asymptotics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 191-208, February.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:191-208
    DOI: 10.1111/1467-9868.00380
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