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序贯估计的渐近理论：微分几何方法AI 解读

Sequential estimation continues observations until the observed sample satisfies a prescribed criterion. Its properties are superior on the average to those of nonsequential estimation in which the number of observations is fixed a priori. A higher-order asymptotic theory of sequential estimation is given in the framework of geometry of multidimensional curved exponential families. This gives a design principle of the second-order efficient sequential estimation procedure.…

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…

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曲指数族的微分几何：曲率与信息损失AI 解读

The differential-geometrical framework is given for analyzing statistical problems related to multi-parameter families of distributions. The dualistic structures of the exponential families and curved exponential families are elucidated from the geometrical viewpoint. The duality connected by the Legendre transformation is thus extended to include two kinds of affine connections and two kinds of curvatures. The second-order information loss is calculated for Fisher-efficient…

渐近辅助性与条件推断的几何理论AI 解读

Differential geometry is applied to the problems of defining higher-order asymptotic ancillarity and of obtaining the asymptotic conditional distribution of an efficient estimator in multiparameter curved exponential families. It is shown that a fundamental role is played in the asymptotic theory of estimation by a one-parameter family of affine connexions and curvatures of subspaces. Asymptotic ancillary statistics of higher order are explicitly constructed with the help of…

渐近辅助性与条件推断的几何理论AI 解读

Differential geometry is applied to the problems of defining higher-order asymptotic ancillarity and of obtaining the asymptotic conditional distribution of an efficient estimator in multiparameter curved exponential families. It is shown that a fundamental role is played in the asymptotic theory of estimation by a one-parameter family of affine connexions and curvatures of subspaces. Asymptotic ancillary statistics of higher order are explicitly constructed with the help of…