On the irregular behavior of LS estimators for asymptotically singular designs
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]*.
Year of publication: |
2006
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Authors: | Pázman, Andrej ; Pronzato, Luc |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 76.2006, 11, p. 1089-1096
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Publisher: |
Elsevier |
Keywords: | Singular design Optimum design Asymptotic normality Consistency LS estimation |
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