Pre-test estimation and design in the linear model. (English) Zbl 0848.62037
Summary: As a robust method against model deviation we consider a pre-test estimation function. To optimize a continuous design for this problem we give an asymptotic risk matrix for the quadratic loss. The risk will then be given by an isotonic criterion function of the asymptotic risk matrix. As an optimization criterion we look for a design that minimizes the maximal risk in the deviation model under the restriction that the risk in the original model does not exceed a given bound. This optimization problem will be solved for the polynomial regression, the deviation consisting in one additional regression function and the criterion function being the determinant.
Keywords:
linear model; D-optimality; robust method against model deviation; pre-test estimation function; continuous design; quadratic loss; isotonic criterion function of the asymptotic risk matrix; polynomial regressionReferences:
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