The Annals of Statistics

Uniform rates of estimation in the semiparametric Weibull mixture model

Hemant Ishwaran

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This paper presents a uniform estimator for a finite-dimensional parameter in the semiparametric Weibull mixture model. The rates achieved by the estimator hold uniformly over shrinking sequences of models much more general than traditional sequences that are required to satisfy a Hellinger differentiable property. We show that these rates are optimal in a class of identified models constrained by a moment condition on the nonparametric mixing distribution.

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Ann. Statist., Volume 24, Number 4 (1996), 1572-1585.

First available in Project Euclid: 17 September 2002

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Zentralblatt MATH identifier

Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties 62P20: Applications to economics [See also 91Bxx]

Weibull semiparametric mixture uniform rates of estimation criterion function


Ishwaran, Hemant. Uniform rates of estimation in the semiparametric Weibull mixture model. Ann. Statist. 24 (1996), no. 4, 1572--1585. doi:10.1214/aos/1032298285.

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  • BEGUN, J. M., HALL, W. J., HUANG, W-M. and WELLNER, J. A. 1983. Information and asy mptotic efficiency in parametric-nonparametric models. Ann. Statist. 11 432 452. Z.
  • BICKEL, P. J. 1982. On adaptive estimation. Ann. Statist. 10 647 671. Z.
  • HECKMAN, J. and SINGER, B. 1984. A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52 271 320. Z.
  • HONORE, B. E. 1990. Simple estimation of a duration model with unobserved heterogeneity. ´ Econometrica 58 453 473.
  • HONORE, B. E. 1994. A note on the rate of convergence of estimators of mixtures of Weibulls. ´ Unpublished manuscript. Z.
  • ISHWARAN, H. 1995. Uniform rates of estimation in the semiparametric Weibull mixture model. Technical Report 278, Laboratory of Research in Statistics and Probability, Carleton Univ. Univ. Ottawa. Z.
  • ISHWARAN, H. 1996. Identifiability and rates of estimation for scale parameters in location mixture models. Ann. Statist. 24 1560 1571. Z.
  • POLLARD, D. 1993. The asy mptotics of a binary choice model. Econometrica. To appear.