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Efficiency of projected score methods in rectangular array asymptotics
Author(s) -
Li Haihong,
Lindsay Bruce G.,
Waterman Richard P.
Publication year - 2003
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00380
Subject(s) - mathematics , estimator , statistics , efficient estimator , minimum variance unbiased estimator , bias of an estimator , maximum likelihood , likelihood function , delta method , upper and lower bounds , consistent estimator , efficiency , mathematical analysis
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.