TY - JOUR
T1 - A Simple GMM Estimator for the Semiparametric Mixed Proportional Hazard Model
AU - Bijwaard, Govert E.
AU - Ridder, Geert
AU - Woutersen, Tiemen
N1 - Funding Information:
We thank Kei Hirano and Nicole Lott for very helpful comments. We also thank seminar participants at the University of Western Ontario, and the Netherlands Interdisciplinary Demographic Institute. This paper replaces the paper Method of Moments Estimation of Duration Models with Exogenous Regressors (2003). Financial support from NORFACE research programme on Migration in Europe – Social, Economic, Cultural and Policy Dynamics is gratefully acknowledged. 1
Publisher Copyright:
© 2013 by Walter de Gruyter Berlin Boston 2013.
PY - 2013
Y1 - 2013
N2 - Ridder and Woutersen (Ridder, G., and T. Woutersen. 2003. "The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model."Econometrica 71: 1579-1589) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspecified distribution of the unobserved heterogeneity. We extend the linear rank estimator (LRE) of Tsiatis (Tsiatis, A. A. 1990. "Estimating Regression Parameters using Linear Rank Tests for Censored Data."Annals of Statistics 18: 354-372) and Robins and Tsiatis (Robins, J. M., and A. A. Tsiatis. 1992. "Semiparametric Estimation of an Accelerated Failure Time Model with Time-Dependent Covariates."Biometrika 79: 311-319) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The efficiency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity.
AB - Ridder and Woutersen (Ridder, G., and T. Woutersen. 2003. "The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model."Econometrica 71: 1579-1589) have shown that under a weak condition on the baseline hazard, there exist root-N consistent estimators of the parameters in a semiparametric Mixed Proportional Hazard model with a parametric baseline hazard and unspecified distribution of the unobserved heterogeneity. We extend the linear rank estimator (LRE) of Tsiatis (Tsiatis, A. A. 1990. "Estimating Regression Parameters using Linear Rank Tests for Censored Data."Annals of Statistics 18: 354-372) and Robins and Tsiatis (Robins, J. M., and A. A. Tsiatis. 1992. "Semiparametric Estimation of an Accelerated Failure Time Model with Time-Dependent Covariates."Biometrika 79: 311-319) to this class of models. The optimal LRE is a two-step estimator. We propose a simple one-step estimator that is close to optimal if there is no unobserved heterogeneity. The efficiency gain associated with the optimal LRE increases with the degree of unobserved heterogeneity.
KW - JEL Classification: C41; C14
KW - counting process
KW - linear rank estimation
KW - mixed proportional hazard
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U2 - 10.1515/jem-2012-0005
DO - 10.1515/jem-2012-0005
M3 - Article
AN - SCOPUS:85080980830
SN - 2156-6674
VL - 2
SP - 1
EP - 23
JO - Journal of Econometric Methods
JF - Journal of Econometric Methods
IS - 1
ER -