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Abstrakty
In this article, we investigate the empirical likelihood method for the additive risk model when the failure times are subject to left-truncation and right-censoring. An empirical likelihood ratio for the p-vector of regression coefficients is defined and it is shown that its limiting distribution is a weighted sum of independent chi-squared distributions with one degree of freedom.This enables one to make empirical likelihood based inference for the regression parameters. Finite sample performance of the proposed methods is illustrated in simulation studies to compare the empirical likelihood method with the normal-approximation-based method.
Czasopismo
Rocznik
Tom
Strony
419--431
Opis fizyczny
Bibliogr. 14 poz., tab.
Twórcy
autor
- Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
autor
- Department of Mathematics & Statistics, University of Minnesota-Duluth, Duluth, MN 55812, U.S.A.
Bibliografia
- [1] O. O. Aalen, A model for nonparametric regression analysis of counting processes, Lecture Notes in Statist. 2, N. Klonecki, A. Kosek and J. Rosiński (Eds.), Springer, New York 1980, pp. 1-25.
- [2] P. K. Andersen and R. D. Gill, Cox's regression model for counting processes: a large sample study, Ann. Statist. 10 (1982), pp. 1100-1120.
- [3] J. D. Buckley, Additive and multiplicative models for survival rates, Biometrics 40 (1984), pp. 51-62.
- [4] D. R. Cox, Regression models and life-tables (with discussion), J. Roy. Statist. Soc. Ser. B 34 (1972), pp. 187-220.
- [5] F. Hall and B. La Scala, Methodology and algorithms of empirical likelihood, Internat. Statist. Rev. 58 (1990), pp. 109-127.
- [6] D. Y. Lin and Z. Ying, Semiparametric analysis of the additive risk model, Biometrika 81 (1994), pp. 61-71.
- [7] T. J. O'Neill, Inconsistency of the misspecified proportional hazards model, Statist. Probab. Lett. 4 (1986), pp. 219-222.
- [8] A. Owen, Empirical likelihood ratio confidence intervals for single functional, Biometrika 75 (1988), pp. 237-249.
- [9] A. Owen, Empirical likelihood ratio confidence regions, Ann. Statist. 18 (1990), pp. 90-120.
- [10] G. Qin and B. Y. Jing, Empirical likelihood for Cox regression model under random censorship, Comm. Statist. Simulation 30 (2001), pp. 79-90.
- [11] D. R. Thomas and G. L. Grunkemeier, Confidence interval estimation of survival probabilities for censored data, J. Amer. Statist. Assoc. 70 (1975), pp. 866-871.
- [12] Q. Y. Wang and B. Y. Jing, Empirical likelihood for a class of functionals of survival distribution with censored data, Ann. Inst. Statist. Math. 53 (2001), pp. 517-527.
- [13] P. S. F. Yip, Y. Zhou, D. Y. Lin and X. Z. Fang, Estimation of population size based on additive hazards models for continuous-time recapture experiments, Biometrics 55 (1999), pp. 904-908.
- [14] M. Zhou, Asymptotic normality of the 'synthetic data' regression estimator for censored survival data, Ann. Statist. 20 (1992), pp. 1002-1021.
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Bibliografia
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