Geometrical Theory of Asymptotic Ancillarity and Conditional Inference
将微分几何应用于多参数弯曲指数族中高阶渐近辅助性的定义以及有效估计量的渐近条件分布的推导，揭示了仿射联络和子空间曲率在估计渐近理论中的关键作用。
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 the geometry. The conditional distribution of an estimator is given in terms of the exponential curvature of the model and the mixture curvature of the ancillary subspaces associated with the estimator.