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Publications Influence

When is B− A− a generalized inverse of AB?☆

- H. Werner
- Mathematics
- 1 October 1994

In practice factorizations of a generalized inverse often arise from factorizations of the matrix which is to be inverted. In addition to full rank factorizations, normal factorizations and singular… Expand

59 2

On Inequality Constrained Generalized Least Squares Selections in the General Possibly Singular

- H. Werner, Cemil Yapar
- Mathematics
- 1 April 1996

This paper deals with the general possibly singular linear model. It is assumed that in addition to the sample information we have some nonstochastic prior information concerning the unknown… Expand

18 2

On extensions of Cramer's rule for solutions of restricted linear systems 1

- H. Werner
- Mathematics
- 1 June 1984

For the unique solution of a special consistent restricted linear system Ax=bx∊M we derive two different determinantal forms, which both reduce to Cramer's classical rule if A is nonsingular. The… Expand

29 1

A BLUE decomposition in the general linear regression model

- H. Werner, Cemil Yapar
- Mathematics
- 1 April 1996

Abstract In this note we consider the general linear regression model (y,Xβ,V|R2β2 = r) where the block partitioned regressor matrix X = (X1 X2) may be deficient in column rank, the dispersion matrix… Expand

25 1

The General Expressions for the Moments of the Stochastic Shrinkage Parameters of the Liu Type Estimator

- F. Akdeniz, G. Styan, H. Werner
- Mathematics
- 1 April 2006

ABSTRACT One of the problems with the Liu estimator is the appropriate value for the unknown biasing parameter d. In this article we consider the optimum value for d and give upper bound for the… Expand

9 1

Generalized inversion and weak bi-complementarity ∗

- H. Werner
- Mathematics
- 1 July 1986

In the literature, complementary matrices have been studied because of their importance in statistics. The present paper shows how this notion can be extended to the concept of weak (hi-)… Expand

14 1

More on partitioned possibly restricted linear regression

- H. Werner, Cemil Yapar
- Mathematics
- 1994

This paper deals with the general partitioned linear regression model where the regressor matrix $X=\pmatrix{X_1 & X_2\cr}$ may be deficient in column rank, the dispersion matrix $V$ is possibly… Expand

25 1

On the matrix monotonicity of generalized inversion

- H. Werner
- Mathematics
- 1 October 1979

Let A, B be two matrices of the same order. We write A>B(A>⩾B) iff A− B is a positive (semi-) definite hermitian matrix. In this paper the well-known result if
A>B>θ, then B−1>A−1> θ
(cf. Bellman… Expand

23 1

Two matrix-based proofs that the linear estimator Gy is the best linear unbiased estimator

- S. Puntanen, G. Styan, H. Werner
- Mathematics
- 1 August 2000

Abstract We offer two matrix-based proofs for the well-known result that the two conditions GX=X and GVQ=0 are necessary and sufficient for Gy to be the traditional best linear unbiased estimator… Expand

44

More on blu estimation in regression models with possibly singular covariances

- H. Werner
- Mathematics
- 1 June 1985

Abstract Consider the general linear regression model E(y) = Aβ, Cov(y) = V, where y is an n × 1 vector of observations, A is a known real n × m matrix, and V is a known dispersion matrix. No rank… Expand

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