Estimation of a Structural Parameter in the Presence of a Large Number of Nuisance Parameters
当冗余参数数量随样本量增加时，Cramer-Rao下界不再可达。本文提出基于信息一致性的新下界，并给出达到该下界的最优估计函数形式，用于评估估计量的效率。
When the number of nuisance parameters increases in proportion to the sample size, the Cramer-Rao bound does not necessarily give an attainable lower bound for the asymptotic variance of an estimator of the structural parameter. The present paper presents a new lower bound under a criterion called information uniformity. The bound is expressed as the inverse of the sum of the partial information and a certain nonnegative term, which is derived by differential-geometrical considerations. The optimal estimating function meeting this lower bound, when it exists, is also obtained in a decomposed form. The first term is the modified score function, and the second term is, roughly speaking, given by the normal component of the mixture covariant derivative of some random variable. Furthermore, special versions of these results are given in concise form, and these are then applied to elucidate the efficiency of some examples.