The Efficiency Bound of the Mixed Proportional Hazard Model

The semiparametric efficiency bound of the mixed proportional hazard model is derived. The density of the model factors in such a way that there exists a complete sufficient statistic for the individual heterogeneity. The efficient score is shown to be the difference between the score in the parametric direction and its conditional expectation given the sufficient statistic. Applying this result to the single-spell Weibull mixed proportional hazard model, it is shown that its information matrix is singular and there cannot exist any '/ -consistent estimator sequence. The information of the multi-spell Weibull mixed proportional hazard model is shown to be nonsingular in general.

[1]  Chris Elbers,et al.  True and Spurious Duration Dependence: The Identifiability of the Proportional Hazard Model , 1982 .

[2]  J. Pfanzagl,et al.  CONTRIBUTIONS TO A GENERAL ASYMPTOTIC STATISTICAL THEORY , 1982 .

[3]  Bo E. Honoré.  Simple estimation of a duration model with unobserved heterogeneity , 1990 .

[4]  Bo E. Honoré,et al.  IDENTIFICATION RESULTS FOR DURATION MODELS WITH MULTIPLE SPELLS OR TIME-VARYING COVARIATES , 1990 .

[5]  J. Powell,et al.  Nonparametric and Semiparametric Methods in Econometrics and Statistics , 1993 .

[6]  P. Bickel,et al.  Mathematical Statistics: Basic Ideas and Selected Topics , 1977 .

[7]  G. Chamberlain.  Asymptotic efficiency in semi-parametric models with censoring , 1986 .

[8]  Tony Lancaster,et al.  ECONOMETRIC METHODS FOR THE DURATION OF UNEMPLOYMENT , 1979 .

[9]  R. Z. Khasʹminskiĭ,et al.  Statistical estimation : asymptotic theory , 1981 .

[10]  W. Newey,et al.  Semiparametric Efficiency Bounds , 1990 .

[11]  John Geweke,et al.  Inference and causality in economic time series models , 1984 .

[12]  Geert Ridder,et al.  The Non-Parametric Identification of Generalized Accelerated Failure-Time Models , 1990 .

[13]  Whitney K. Newey,et al.  Adaptive estimation of regression models via moment restrictions , 1988 .

[14]  C. Stein.  Efficient Nonparametric Testing and Estimation , 1956 .

[15]  Charles F. Manski,et al.  Adaptive estimation of non–linear regression models , 1984 .

[16]  Tony Lancaster,et al.  The Econometric Analysis of Transition Data. , 1992 .

[17]  G. Chamberlain.  Asymptotic efficiency in estimation with conditional moment restrictions , 1987 .

[18]  J. Heckman,et al.  The Identifiability of the Proportional Hazard Model , 1984 .

[19]  J. Pfanzagl.  Estimation in semiparametric models , 1990 .

[20]  P. Bickel.  On Adaptive Estimation , 1982 .

[21]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .