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∗.
Liste complète des métadonnées

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00416062
Contributor : Luc Pronzato <>
Submitted on : Friday, September 11, 2009 - 5:55:45 PM
Last modification on : Monday, March 18, 2019 - 6:36:51 PM
Document(s) archivé(s) le : Tuesday, June 15, 2010 - 11:34:54 PM

File

Pazman_P_SPL2005.pdf
Files produced by the author(s)

Identifiers

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⟩

Share

Metrics

Record views

331

Files downloads

64