Sankhya: The Indian Journal of Statistics

1996, Volume 58, Series B, Pt. 3, pp. 338--351

THE LINEAR ZERO FUNCTIONS APPROACH TO LINEAR MODELS

By

POCHIRAJU BHIMASANKARAM , Indian Statistical Institute, Calcutta

and

DEBASIS SENGUPTA, University of  California, Santa Barbara

SUMMARY.  In this paper we develop the theory of linear models using the properties of Linear Zero Functions. It is shown that all the major results on inference can be derived using these properties and simple vector arguments. The general philosophy of the development is to enhance understanding of the problem by appealing to the intuition of the reader. A common feature of the results derived here is that they integrate the singular dispersion case into mainstream. This is achieved without use of heavy algebra. On the contrary, most of the derivations are simpler than the conventional ones. Nevertheless, the extension of some of the results to the singular dispersion case are new. 

AMS (1991) subject classification.  62J05.

Key words and phrases. Linear estimation, residual sum of squares, vector space, singular model, linear restriction, nuisance parameter.

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