Semi-nonparametric Interval-censored Mixed Proportional Hazard Models: Identification and Consistency Results∗

In this paper I propose to estimate distributions on the unit interval semi-nonparametrically using orthonormal Legendre polynomials. This approach will be applied to the interval censored mixed proportional hazard (ICMPH) model, where the distribution of the unobserved heterogeneity is modeled semi-nonparametrically. Various conditions for the nonparametric identification of the ICMPH model are derived. I will prove general consistency results for M estimators of (partly) non-Euclidean parameters under weak and easy-to-verify conditions, and specialize these results to sieve estimators. Special attention is paid to the case where the support of the covariates is finite. ∗Econometric Theory, 2008 (in print). †Previous versions of this paper have been presented at the Universidade Federal do Ceara, Brazil, Texas Econometrics Camp 2005, the 2005 World Congress of the Econometric Society, Ohio State University, Cemapre, Lisbon, and Brown University. The helpful comments of Aleksandr Vashchilko, Yuichi Kitamura and two referees are gratefully acknowledged. Address correspondence to Herman J. Bierens, Department of Economics, Pennsylvania State University, 608 Kern Graduate Building, University Park, PA 16802; e-mail: [email protected].