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- Title
Estimations of parametric functions under a system of linear regression equations with correlated errors.
- Authors
Tian, Yong
- Abstract
Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool — the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators (BLUEs) of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold.
- Subjects
REGRESSION analysis; GENERALIZED inverses of linear operators; NUMERICAL solutions to equations; VECTOR algebra; KRONECKER products; RANDOM matrices
- Publication
Acta Mathematica Sinica, 2010, Vol 26, Issue 10, p1927
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-010-8434-7