Efficiency in Neyman-Scott Type Problems under Rectangular Array Asymptotics
Haihong Li , Bruce G. Lindsay and Richard P. Waterman
This paper considers a "rectangular array" asymptotic embedding for multi- strata data sets, in which both the number of strata and the number of within-strata replications increase, and at the same rate. It is shown that under this embedding the MLE is consistent but not efficient due 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 variance that attains the Cramer-Rao lower bound. The adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator.
Key Words Asymptotic theory; Nuisance parameters; Neyman-Scott problem; Rectangular array; Square array; Projected score