# SFB 303 Discussion Paper No. B-300

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

**Title:** On Inequality Constrained Generalized Least Squares
Selections in the General Possibly Singular Gauss-Markov Model: A Projector
Theoretical Approach

**Abstract:** 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 regression
coefficients that can be expressed in form of linear independent inequality
constraints. Since these constraints are part and parcel of the model
the inequality constrained generalized least squares (ICGLS) problem
arises that contains some unknown aspects up to now. Based on a projector
theoretical approach we show in this paper how the set of ICGLS selections
under the constrained model is related to the set of GLS selections under
the associated unconstrained model. As a by-product we obtain an interesting
method for determining an ICGLS selection from a GLS selection. The insights
gained from our considerations might also be useful in a future study
of the statistical properties of ICGLS estimators. Certain special model
cases are also considered. Some of the results discussed in [29] and [7]
are reobtained.

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

**JEL-Classification-Number**:

**Creation-Date:** 1994

**URL:**
../1994/b/bonnsfb300.pdf
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