Equalities between OLSE, BLUE and BLUP in the linear model

被引：20

作者：

Haslett, Stephen J. ^{[1
]}

Isotalo, Jarkko ^{[2
]}

Liu, Yonghui ^{[3
]}

Puntanen, Simo ^{[4
]}

机构：

[1] Massey Univ, Inst Fundamental Sci, Palmerston North, New Zealand

[2] Univ Helsinki, Dept Forest Sci, FIN-00014 Helsinki, Finland

[3] Shanghai Finance Univ, Dept Appl Math, Shanghai 201209, Peoples R China

[4] Univ Tampere, Sch Informat Sci, Tampere 33014, Finland

来源：

STATISTICAL PAPERS | 2014年 / 55卷 / 02期

关键词：

Best linear unbiased estimator; Best linear unbiased predictor; Gauss-Markov model; Generalized inverse; Linear model; Ordinary least squares; SMALL-AREA ESTIMATION; LEAST-SQUARES; UNBIASED PREDICTOR; SPATIAL-PATTERNS; EUCLIDEAN NORM; RURAL POVERTY; SIMPLE FORMS; DIFFERENCE; ESTIMATORS; MATRIX;

D O I：

10.1007/s00362-013-0500-7

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：

We consider equalities between the ordinary least squares estimator (), the best linear unbiased estimator () and the best linear unbiased predictor () in the general linear model extended with the new unobservable future value of the response whose expectation is . Our aim is to provide some new insight and new proofs for the equalities under consideration. We also collect together various expressions, without rank assumptions, for the and provide new results giving upper bounds for the Euclidean norm of the difference between the and and between the and . A remark is made on the application to small area estimation.

引用

页码：543 / 561

页数：19

共 45 条

[11] Christensen R, 2011, SPRINGER TEXTS STAT, P1, DOI 10.1007/978-1-4419-9816-3
[12] Davidson R., 2004, ECONOMETRIC THEORY M
[13] Micro-level estimation of poverty and inequality
Elbers, C
Lanjouw, JO
Lanjouw, P
[J]. ECONOMETRICA, 2003, 71 (01) : 355 - 364
[14] Elbers C., 2004, Poverty and Inequality in Brazil
[15] Simple forms of the best linear unbiased predictor in the general linear regression model
Elian, SN
[J]. AMERICAN STATISTICIAN, 2000, 54 (01) : 25 - 28
[16] Exploring the spatial variation of food poverty in Ecuador
Farrow, A
Larrea, C
Hyman, G
Lema, G
[J]. FOOD POLICY, 2005, 30 (5-6) : 510 - 531
[17] BEST LINEAR UNBIASED PREDICTION IN GENERALIZED LINEAR-REGRESSION MODEL
GOLDBERGER, AS
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1962, 57 (298) : 369 - &
[18] The general Gauss-Markov model with possibly singular dispersion matrix
Gross, J
[J]. STATISTICAL PAPERS, 2004, 45 (03) : 311 - 336
[19] Harville David A, 1998, Matrix algebra from a statistician's perspective
[20] SMALL-AREA ESTIMATION OF POVERTY: THE AID INDUSTRY STANDARD AND ITS ALTERNATIVES
Haslett, S. J.
Jones, G.
[J]. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 2010, 52 (04) : 341 - 362

← 1 2 3 4 5 →