非线性半参数统计模型估计函数的几何方法

摘要

The probability density function family of nonlinear semi-parametric statistical model are considered as a statistical manifold.Using the methods of differential geometry to construct Hilbert space corresponding to nonlinear semiparametric model, and then study some questions of estimation function. Using the subspace spanned by two kinds of score function to decompose the Hilbert space orthogonally,and then discuss the set of the estimated function is located, and how to select the best estimate of function problems. Finally, through the analysis of examples to verify the effectiveness of this method.%将非线性半参数统计模型的概率密度函数族视为统计流形，利用微分几何方法，建立非线性半参数统计模型相对应的Hilbert 空间，进而研究非线性半参数统计模型的估计函数问题。利用两类得分函数张成的子空间对 Hilbert 空间进行正交分解，进而讨论估计函数所在的集合，以及如何选取最优估计函数的问题。最后，通过实例分析来验证此方法的有效性。