Sankhya: The Indian Journal of Statistics

1995, Volume 57, Series A, Pt. 1, pp. 137--153

OPTIMAL CHOICE OF A NEW OBSERVATION IN A LINEAR MODEL

By

 DEBASIS SENGUPTA, Indian Statistical Institute

SUMMARY.  The problem of designing a new observation in a general linear model is considered. Assuming that the design of the earlier observations cannot be altered, the choice of the new observation is aimed at maximizing either the information about an estimate parametric function or the average information about a few such functions. A closed form solution is obtained in the first case, while an algorithm is provided in the case of the latter - both in the presence of a quadratic constraint. Typically the problem reduces to the maximization of the ratio of two quadratic functions with the variable vectors in the numerator and the denominator lying in mutually orthogonal spaces. Selection from a finite set of candidate designs is also discussed and the methods are illustrated via examples.

AMS (1991) subject classification.  62J05, 62K05.

Key words and phrases. Optimal design of experiments, unified theory of least squares estimation, recursive inference.

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