On the irregular behavior of LS estimators for asymptotically singular designs

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 θ, or of a function of interest h(θ), may be impossible with the singular design ξ∗. Depending on how ξ∗ is approached by the empirical measure ξn of the design points, with n the number of observations, consistency is achieved but the speed of convergence may depend on ξn and on the value of θ. Even in situations where convergence is in 1/√n and the asymptotic distribution of the estimator of θ or h(θ) is normal, the asymptotic variance may still differ from that obtained from ξ∗.
Type de document :
Article dans une revue
Statistics and Probability Letters, Elsevier, 2006, 76, pp.1089-1096. <10.1016/j.spl.2005.12.010>
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00416062
Contributeur : Luc Pronzato <>
Soumis le : vendredi 11 septembre 2009 - 17:55:45
Dernière modification le : samedi 12 septembre 2009 - 08:11:51
Document(s) archivé(s) le : mardi 15 juin 2010 - 23:34:54

Fichier

Pazman_P_SPL2005.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Andrej Pazman, Luc Pronzato. On the irregular behavior of LS estimators for asymptotically singular designs. Statistics and Probability Letters, Elsevier, 2006, 76, pp.1089-1096. <10.1016/j.spl.2005.12.010>. <hal-00416062>

Partager

Métriques

Consultations de
la notice

168

Téléchargements du document

37