On the irregular behavior of LS estimators for asymptotically singular designs

Andrej Pázman and Luc Pronzato

Statistics & Probability Letters, 2006, vol. 76, issue 11, 1089-1096

Abstract: Optimum design theory sometimes yields singular designs. An example with a linear regression model often mentioned in the literature is used to illustrate the difficulties induced by such designs. The estimation of the model parameters [theta], or of a function of interest h([theta]), may be impossible with the singular design [xi]*. Depending on how [xi]* is approached by the empirical measure [xi]n of the design points, with n the number of observations, consistency is achieved but the speed of convergence may depend on [xi]n and on the value of [theta]. Even in situations where convergence is in and the asymptotic distribution of the estimator of [theta] or h([theta]) is normal, the asymptotic variance may still differ from that obtained from [xi]*.

Keywords: Singular; design; Optimum; design; Asymptotic; normality; Consistency; LS; estimation (search for similar items in EconPapers)
Date: 2006
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