2016/12/21 by Xu, Ximing, Reid, Nancy, Xu, Libai
#FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1612.06967
Does the asymptotic variance of the maximum composite likelihood estimator of a parameter of interest always decrease when the nuisance parameters are known? Will a composite likelihood necessarily become more efficient by incorporating addi- tional independent component likelihoods, or by using component likelihoods with higher dimension? In this note we show through illustrative examples that the an- swer to both questions is no, and indeed the opposite direction might be observed. The role of information bias is highlighted to understand the occurrence of these paradoxical phenomenon.