一类矩阵椭球等高分布在数据不完全的参数估计

The Estimation of Parameters for A Class of Matrix Elliptically Contoured Distributions in Incomplete Data

对于一类矩阵椭球等高分布在数据不完全(缺失数据)情况下,本文导出了未知参数具有MLE条件的估计,并证明■、■分别为μ_1、μ_2的无偏估计、相合估计及较有效估计。

The estimation of parameters for a class of matrix elliptically contoureddistributions (MECD) in incomplete data is discussed. In the case of i.i.d. expo-nential-family, EM-algorithm is feasible and effective, but not so good inMECD. Using the conditional expectation of missing values given all known data asthe estimators of missing values, by the results of MECD,we give estimatorsin Theorem 1. Under certain general regularity conditions, we prove that μ_1、μ_2are unbised and consistent estimators of μ_1、μ_2 respectively and that the potentialgain in precision by using the incomplete data is attainable.