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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
Biographic References:
Stute, Winfried
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[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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