Université de Lausanne
Ecole des HEC
Département d'économétrie et d'économie politique

Mardi 11 décembre 2007, 17h00
Extranef, Dorigny, salle 126

Olivier SCAILLET
(HEC, University of Geneva)

Tikhonov Regularization for Nonparametric Instrumental Variable Estimators

Abstract
We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in an additively separable model. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivative. We derive the asymptotic Mean Integrated Square Error, the rate of convergence and the pointwise asymptotic normality under a regularization parameter depending on sample size. The optimal value of the regularization parameter is characterized. We illustrate our theoretical findings and the small sample properties with simulation results in a numerical example. We also discuss two data driven selection procedures of the regularization parameter via a spectral representation and a subsampling approximation of the MISE. Finally, we provide an empirical application to
estimation of an Engel curve.

Site web du séminaire (avec texte en ligne): http://www.hec.unil.ch/deep/evenements-english/e-sem-all-2007-08.htm