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On the irregular behavior of LS estimators for asymptotically singular designs

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  • Pázman, Andrej
  • Pronzato, Luc

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]*.

Suggested Citation

  • Pázman, Andrej & Pronzato, Luc, 2006. "On the irregular behavior of LS estimators for asymptotically singular designs," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1089-1096, June.
  • Handle: RePEc:eee:stapro:v:76:y:2006:i:11:p:1089-1096
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    References listed on IDEAS

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    1. Valery Fedorov & Werner Müller, 1997. "Another view on optimal design for estimating the point of extremum in quadratic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 46(1), pages 147-157, January.
    2. Schwabe, Rainer, 1997. "Maximin efficient designs another view at D-optimality," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 109-114, September.
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