We examined the asymptotic efficiency of the ML estimator of the treatment and the treatment by period interaction effect for three two-treatment designs: a parallel, an extended parallel, and a crossover design.
For each pair of ranges of the intraclass correlations, the asymptotic efficiency of each design versus the most efficient design is given within brackets.
The local asymptotic power of the tests is also investigated using the local approximation of the power function or Pitman asymptotic efficiency. Finite sample empirical (size and power) performance comparisons are investigated by Monte Carlo simulations.
We discuss the variants of Fisher's exact test for the Q-symmetry contingency table in Section 3 and asymptotic power analysis (i.e., consistency of the tests and their asymptotic efficiency) in Section 4 and provide an extensive empirical performance analysis by Monte Carlo simulations in Section 5.
This makes the comparison of the tests inappropriate even for large samples; however, under specific alternatives and assumptions, we can estimate asymptotic efficiency scores, such as those of Pitman asymptotic efficiency.
IV asymptotics are then discussed, with special consideration given to the question of optimal instruments and asymptotic efficiency
in the special case of 2SLS, providing a natural transition to the material on GMM estimation and inference covered in Chapters 21 and 22.
Once the order of autocorrelation is determined, one can use various procedures to improve the asymptotic efficiency
of the estimates.