Nonparametric Estimation of Bivariate Distribution using Concomitants of Order Statistics
Survival and reliability studies often involve paired observations subject to various forms censoring. In this paper, we discuss the analysis the paired survival data under type II censoring. We develop a nonparametric estimator of bivariate distribution function using concomitants of order statistics for type II censored survival data. Strong consistency and asymptotic normality of the estimator are established. A simulation study is carried out to assess the finite sample behaviour of the estimator. Finally, we illustrate the estimation procedure using two real life data sets.
Key-wordsBivariate distribution Concomitants of order statistics Kaplan-Meier estimator Type II censoring Nonparametric estimation
AMS Subject Classification62G05 62P10
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- Beran, R., 1981. Nonparametric regression with randomly censored survival data. Technical report, University of California at Berkeley, Berkeley.Google Scholar
- Byar, D.P., 1980. The veteran’s administration study of chemoprophylaxis for recurrent stage i bladder tumors: comparisons of placebo, pyridoxine and topical thiotepa. In Bladder Tumors and Other Topics in Urological Oncology, Pavone-Macaluso, M.M., Smith, P.H. and Edlsmyn, F. (Editors), Plenum, New York, pp. 363–370.CrossRefGoogle Scholar
- Campbell, G., Foldes, A., 1982. Large sample properties of non-parametric bivariate estimators with censored data. In Nonparametric Statistical Inference, Gnedenko, B.V., Puri, M.L., Vincze, I. (Editors), North-Holland, Amsterdam, pp. 103–121.Google Scholar
- Duffy, D.L., Martin, N.G., Mathews, J.D., 1990. Appendectomy in Australian twins. American Journal of Human Genetics, 47, 590–592.Google Scholar
- Nagaraja, H.N., 2003. Functions of concomitants of order statistics. Journal of Indian Society for Probability and Statistics, 7, 16–23.Google Scholar
- Yang, S.S., 1981. Linear functions of concomitants of order statistics with application to non-parametric estimation of a regression function. Journal of the American Statistical Association, 84, 1065–1073.Google Scholar