结构关系度量误差模型中参数估计的渐近性质  

ASYMPTOTIC PROPERTIES OF AN ESTIMATOR IN NONLINEAR ERRORS-IN-VARIABLE REGRESSION MODEL

作　　者：徐松[1] 

机构地区：[1]北京师范大学数学系,北京100875

出　　处：《北京师范大学学报（自然科学版）》1998年第4期462-467,共6页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金!39130080

摘　　要：考虑结构关系度量误差模型其中P维向量Y，q维向量Z为可观测随机变量，X为不可观测随机变量，U，F分别表示相应的度量误差，H（x，θ）是未知参数θ的非线性函数，参数空间是Rm中的有界闭区间．假设X,U,F相互独立，X服从包括正态分布的一类椭球等高分布，U～N（0，U），F～N（0，F），F＞0已知．在一定条件下给出了θ的一个强相合且渐近正态估计．Consider the following EIVR model Where Y is a p-dimen-sional colunm vector, Z is a q-dimensional colunm vector, X is a random vector of true (latent) predictor variables, the random vector F contains the errors of measurement for the predictors, and the random vector U contains both measurement errors and random equation errors for the depended variables. It is assumed that X, U and F are mutually statistically independent, where X has a elliptically coniced distribution,is known. Under certain conditions, an estimator having properties of strong consistency and asymptotic normality is proposed for θ.

关 键 词：度量误差模型 参数估计 渐近性质 结构关系 

分 类 号：O211.67[理学—概率论与数理统计]