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An odyssey to incomplete data: Winfried Stute’s contribution to survival analysis. (English) Zbl 1383.62008
Ferger, Dietmar (ed.) et al., From statistics to mathematical finance. Festschrift in honour of Winfried Stute. Cham: Springer (ISBN 978-3-319-50985-3/hbk; 978-3-319-50986-0/ebook). 3-23 (2017).
Summary: In this article, we revisit Winfried Stute’s contributions to survival analysis, which constitute a significant portion of his publications. Instead of a comprehensive review of his work in survival analysis, we focus on four papers that are fundamental by themselves.
For the entire collection see [Zbl 1383.62010].
##### MSC:
 62-03 History of statistics 01A70 Biographies, obituaries, personalia, bibliographies 62N01 Censored data models 62N05 Reliability and life testing
Stute, Winfried
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##### References:
 [1] Azarang, L., J. de Uña-Álvarez, and W. Stute (2013). The jackknife estimate of covariance under censorship when covariables are present. Discussion Papers in Statistics and Operations Research, Report 13/04, Universidad de Vigo. [2] Breslow, N. and J. Crowley (1974). A large sample study of the life table and product limit estimates under random censorship. $$Ann. Statist.$$ $$2$$ (3), 437-453. · Zbl 0283.62023 [3] Buckley, J. and I. James (1979). Linear regression with censored data. $$Biometrika$$ $$66$$ (3), 429-436. · Zbl 0425.62051 [4] Chao, M.-T. and S.-H. Lo (1988). Some representations of the nonparametric maximum likelihood estimators with truncated data. $$Ann. Statist.$$ $$16$$ (2), 661-668. · Zbl 0645.62048 [5] Diehl, S. and W. Stute (1988). Kernel density and hazard function estimation in the presence of censoring. $$J. Multivariate Anal.$$ $$25$$ (2), 299-310. · Zbl 0661.62028 [6] Dikta, G., B. Kurtz, and W. Stute (1989). Sequential fixed-width confidence bands for distribution functions under random censoring. $$Metrika$$ $$36$$ (1), 167-176. · Zbl 0698.62081 [7] Gill, R. (1980). Censoring and stochastic integrals. $$Stat. Neerl.$$ $$34$$ (2), 124-124. Censoring and stochastic integrals. Math. Centre Tract 124, Math. Centrum, Amsterdam. · Zbl 0456.62003 [8] Gill, R. (1983). Large sample behaviour of the product-limit estimator on the whole line. $$Ann. Statist.$$ $$11$$ (1), 49-58. · Zbl 0518.62039 [9] Gürler, Ü., W. Stute, and J.-L. Wang (1993). Weak and strong quantile representations for randomly truncated data with applications. $$Statist. Probab. Lett.$$ $$17$$ (2), 139-148. · Zbl 0797.62039 [10] He, S. and G. L. Yang (1998a). Estimation of the truncation probability in the random truncation model. $$Ann. Statist.$$ $$26$$ (3), 1011-1027. · Zbl 0929.62036 [11] He, S. and G. L. Yang (1998b). The strong law under random truncation. $$Ann. Statist.$$ $$26$$ (3), 992-1010. · Zbl 0929.62037 [12] Keiding, N. and R. D. Gill (1990). Random truncation models and markov processes. $$Ann. Statist.$$ $$18$$ (2), 582-602. · Zbl 0717.62073 [13] Lo, S.-H. and K. Singh (1986). The product-limit estimator and the bootstrap: Some asymptotic representations. $$Probab. Theory Related Fields$$ $$71$$ (3), 455-465. · Zbl 0561.62032 [14] Lynden-Bell, D. (1971). A method of allowing for known observational selection in small samples applied to 3cr quasars. $$Mon. Not. R. Astron. Soc.$$ $$155$$ (1), 95-118. [15] Major, P. and L. Rejto (1988). Strong embedding of the estimator of the distribution function under random censorship. $$Ann. Statist.$$ $$16$$ (3), 1113-1132. · Zbl 0667.62024 [16] Neveu, J. (1975). $$Discrete-parameter martingales$$ . North-Holland, Amsterdam. [17] Schick, A., V. Susarla, and H. Koul (1988). Efficient estimation of functionals with censored data. $$Stat. Risk Model.$$ $$6$$ (4), 349-360. · Zbl 0686.62024 [18] Sen, A. and W. Stute (2014). Identification of survival functions through hazard functions in the clayton-family. $$Statist. Probab. Lett.$$ $$87$$ , 94-97. · Zbl 1320.62211 [19] Strzalkowska-Kominiak, E. and W. Stute (2010). On the probability of holes in truncated samples. $$J. Statist. Plann. Inference$$ $$140$$ (6), 1519-1528. · Zbl 1185.62171 [20] Stute, W. (1976). On a generalization of the glivenko-cantelli theorem. $$Z. Wahrscheinlichkeit.$$ $$35$$ (2), 167-175. · Zbl 0324.60001 [21] Stute, W. (1982). The oscillation behavior of empirical processes. $$Ann. Probab.$$ $$10$$ (1), 86-107. · Zbl 0489.60038 [22] Stute, W. (1993a). Almost sure representations of the product-limit estimator for truncated data. $$Ann. Statist.$$ $$21$$ (1), 146-156. · Zbl 0770.62027 [23] Stute, W. (1993b). Consistent estimation under random censorship when covariables are present. $$J. Multivariate Anal.$$ $$45$$ (1), 89-103. · Zbl 0767.62036 [24] Stute, W. (1994a). The bias of kaplan-meier integrals. $$Scand. J. Stat.$$ $$21$$ (4), 475-484. · Zbl 0812.62042 [25] Stute, W. (1994b). Convergence of the kaplan-meier estimator in weighted sup-norms. $$Statist. Probab. Lett.$$ $$20$$ (3), 219-223. · Zbl 0798.62066 [26] Stute, W. (1994c). Improved estimation under random censorship. $$Commun. Stat. Theor. M.$$ $$23$$ (9), 2671-2682. · Zbl 0825.62226 [27] Stute, W. (1994d). Strong and weak representations of cumulative hazard function and kaplan-meier estimators on increasing sets. $$J. Statist. Plann. Inference$$ $$42$$ (3), 315-329. · Zbl 0815.62016 [28] Stute, W. (1994e). U-statistic processes: A martingale approach. $$Ann. Probab.$$ $$22$$ (4), 1725-1744. · Zbl 0832.62043 [29] Stute, W. (1995a). The central limit theorem under random censorship. $$Ann. Statist.$$ $$23$$ (2), 422-439. · Zbl 0829.62055 [30] Stute, W. (1995b). The statistical analysis of kaplan-meier integrals. $$Lecture Notes-Monograph Series$$ $$27$$ , 231-254. · Zbl 0876.62028 [31] Stute, W. (1996a). Distributional convergence under random censorship when covariables are present. $$Scand. J. Stat.$$ $$23$$ (4), 461-471. · Zbl 0903.62045 [32] Stute, W. (1996b). The jackknife estimate of variance of a kaplan-meier integral. $$Ann. Statist.$$ $$24$$ (6), 2679-2704. · Zbl 0878.62027 [33] Stute, W. and J.-L. Wang (1993a). Multi-sample u-statistics for censored data. $$Scand. J. Stat.$$ $$20$$ (4), 369-374. · Zbl 0799.60031 [34] Stute, W. and J.-L. Wang (1993b). The strong law under random censorship. $$Ann. Statist.$$ $$21$$ (3), 1591-1607. · Zbl 0785.60020 [35] Stute, W. and J.-L. Wang (1994). The jackknife estimate of a kaplan-meier integral. $$Biometrika$$ $$81$$ (3), 602-606. · Zbl 0809.62037 [36] Stute, W. and J.-L. Wang (2008). The central limit theorem under random truncation. $$Bernoulli$$ $$14$$ (3), 604-622. · Zbl 1157.62017 [37] Susarla, V. and J. Van Ryzin (1980). Large sample theory for an estimator of the mean survival time from censored samples. $$Ann. Statist.$$ $$8$$ (5), 1002-1016. · Zbl 0455.62030 [38] Wang, J.-L. (1995). M-estimators for censored data: strong consistency. $$Scand. J. Stat.$$ $$22$$ (2), 197-205. · Zbl 0872.62060 [39] Wang, M.-C., N. P. Jewell, and W.-Y. Tsai (1986). Asymptotic properties of the product limit estimate under random truncation. $$Ann. Statist.$$ $$14$$ (4), 1597-1605. · Zbl 0656.62048 [40] Woodroofe, M. (1985). Estimating a distribution function with truncated data. $$Ann. Statist.$$ $$13$$ (1), 163-177. · Zbl 0574.62040 [41] Yang, S. (1994). A central limit theorem for functionals of the kaplanmeier estimator. $$Statist. Probab. Lett.$$ $$21$$ (5), 337 - 345. · Zbl 0810.60016 [42] Ying, Z. (1989). A note on the asymptotic properties of the product-limit estimator on the whole line. $$Statist. Probab. Lett.$$ $$7$$ (4), 311-314. · Zbl 0675.62034
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