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无限多个干扰参数下的估计：估计函数的几何AI 解读

When there exist nuisance parameters whose number increases in proportion to that of independent observations, it is in general difficult to get a consistent or efficient estimator of a common structural parameter. The present paper proposes a new theory based on a vector bundle consisting of certain random variables over the statistical model. Structures and properties of estimating functions are elucidated in the class of consistent estimators. A necessary and sufficient…

存在大量干扰参数时结构参数的估计AI 解读

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…

大量干扰参数存在时的结构参数估计AI 解读

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…