SFB 303 Discussion Paper No. B-326

Author: Werner, Hans Joachim, and Cemil Yapar
Title: A BLUE Decomposition in the General Linear Regression Model
Abstract: In this note we consider the {\it general} linear regression model $(y,\ X\beta,\ V\mid\ R_2\beta_2=r)$ where the block partitioned regressor matrix $X=\pmatrix{X_1 & X_2\cr}$ may be deficient in column rank, the dispersion matrix $V$ is possibly singular, $\beta^t=\pmatrix{\beta_1^t & \beta_2^t\cr}$ - being partitioned according to $X$ - is the vector of unknown regression coefficients, and $\beta_2$ is possibly subject to consistent linear constraints $R_2\beta_2=r$. Of much interest to us is the {\it traditional} BLUE {\it (best linear unbiased estimator)} of $X\beta$. We show how this traditional BLUE can obtained from the traditional BLUE of $X_1\beta_1$ in the related model $(y,\ X_1\beta_1,\ V)$. Some properties of the dispersion matrix of the traditional BLUE of $X\beta$ are also given.
Keywords: Linear regression model, rank deficiency, linear constraints, traditional BLUE, dispersion, g-inversion.
JEL-Classification-Number: C20
Creation-Date: 1995
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