# SFB 303 Discussion Paper No. B-301

**Author:** Werner, Hans Joachim, and Cemil Yapar

**Title:** More on partitioned possibly restricted linear regression

**Abstract:** 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 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 equality or inequality
restrictions. In particular, we are interested in the set of {\it generalized
least squares (GLS) selections} for $\beta_2$. Inspired by Aigner and
Balestra [1], as well as by Nurhonen and Puntanen [2], we also consider
a specific reduced model and describe a scenario under which the set of
GLS selections for $\beta_2$ under the reduced model equals the set of
GLS selections for $\beta_2$ under the original full model. The results
obtained in [2] and [1] for the unrestricted {\it standard} (full rank)
regression model are reobtained as special cases.

**Keywords:** Gauss-Markov model, singular model, perfect
multicollinearity, partitioned linear regression, linear equality constraints,
linear inequality constraints, constrained generalized least squares
selections, oblique projectors, generalized inverses.

**Keywords**:

**JEL-Classification-Number**: C20

**Creation-Date**: 1994

**URL**:
../1994/b/bonnsfb301.pdf
SFB 303 Homepage

17.02.1998, © Webmaster