The uniform central limit theorem for the Kaplan-Meier integral process

Bae, Jong-Sig; SungYeun, Kim

doi:10.1017/s0004972700037266

Cited by 2 publications

(2 citation statements)

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“…The pointwise weak convergence of

{\overset{M}{true}}_{n}^{false(j false)} ((), s)

can now be extended to uniform weak convergence over the class defined in , following similar arguments to those given by Bae & Kim (). The proof of the following theorem is found in Appendix B.…”

Section: Asymptotic Properties Of the Modified Empirical Mgf And Derimentioning

confidence: 98%

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An empirical saddlepoint approximation based method for smoothing survival functions under right censoring

et al. 2019

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The Kaplan–Meier (KM) estimator is ubiquitously used for estimating survival functions, but it provides only a discrete approximation at the observation times and does not deliver a proper distribution if the largest observation is censored. Using KM as a starting point, we devise an empirical saddlepoint approximation‐based method for producing a smooth survival function that is unencumbered by choice of tuning parameters. The procedure inverts the moment generating function (MGF) defined through a Riemann–Stieltjes integral with respect to an underlying mixed probability measure consisting of the discrete KM mass function weights and an absolutely continuous exponential right‐tail completion. Uniform consistency, and weak and strong convergence results are established for the resulting MGF and its derivatives, thus validating their usage as inputs into the saddlepoint routines. Relevant asymptotic results are also derived for the density and distribution function estimates. The performance of the resulting survival approximations is examined in simulation studies, which demonstrate a favourable comparison with the log spline method (Kooperberg & Stone, 1992) in small sample settings. For smoothing survival functions we argue that the methodology has no immediate competitors in its class, and we illustrate its application on several real data sets. The Canadian Journal of Statistics 47: 238–261; 2019 © 2019 Statistical Society of Canada

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“…The pointwise weak convergence of

{\overset{M}{true}}_{n}^{false(j false)} ((), s)

Section: Asymptotic Properties Of the Modified Empirical Mgf And Derimentioning

confidence: 98%

“…In parallel to what was done for consistency, this will also be extended to uniform weak convergence over the class defined in by dealing with the relevant empirical processes. This part of the development will largely use the results of Bae & Kim ().…”

Section: Asymptotic Properties Of the Modified Empirical Mgf And Derimentioning

confidence: 99%