The general Gauss-Markov model with possibly singular dispersion matrix

被引:40
作者
Gross, J [1 ]
机构
[1] Univ Dortmund, Dept Stat, D-44221 Dortmund, Germany
关键词
D O I
10.1007/BF02777575
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Linear models with possibly singular dispersion (variance-covariance) matrix of the vector of disturbances have been considered in the literature since the late sixties. In this paper we give a survey of important results and consequences without a claim to completeness. Proofs are given for the results in Sections 2 to 5. 1 Notation 2 The General Gauss-Markov Model 3 Best Linear Unbiased Estimation 4 Quadratic Unbiased Estimation 5 Testing a Linear Hypothesis 6 Further Aspects of Linear Estimation.
引用
收藏
页码:311 / 336
页数:26
相关论文
共 36 条
[1]  
[Anonymous], 1968, SANKHYA SER A
[2]  
[Anonymous], 1971, GEN INVERSES MATRICE
[3]  
[Anonymous], SANKHYA B
[4]   ADMISSIBLE LINEAR ESTIMATORS OF AN ARBITRARY VECTOR OF PARAMETRIC FUNCTIONS IN THE GENERAL GAUSS-MARKOV MODEL [J].
BAKSALARY, JK ;
MARKIEWICZ, A .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1990, 26 (02) :161-171
[5]   A MATRIX INEQUALITY AND ADMISSIBILITY OF LINEAR ESTIMATORS WITH RESPECT TO THE MEAN-SQUARE ERROR MATRIX CRITERION [J].
BAKSALARY, JK ;
MARKIEWICZ, A .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 112 :9-18
[6]   A STUDY OF THE INFLUENCE OF THE NATURAL RESTRICTIONS ON ESTIMATION PROBLEMS IN THE SINGULAR GAUSS-MARKOV MODEL [J].
BAKSALARY, JK ;
RAO, CR ;
MARKIEWICZ, A .
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1992, 31 (03) :335-351
[7]  
Baksalary JK, 1989, STAT DATA ANAL INFER, P355
[8]   ON LEAST-SQUARES WITH INSUFFICIENT OBSERVATIONS [J].
CHIPMAN, JS .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1964, 59 (308) :1078-&
[9]  
CHIPMAN JS, 1976, GENERALIZED INVERSES, P549
[10]  
CHRISTENSEN R, 1990, AM STAT, V44, P192