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Year:: 2023
Contributor:: Provost, Nathan Thomas (creator); Steingrimsson, Jon (thesis advisor); Oganisian, Arman (reader); Brown University. Biostatistics (sponsor)
Genre:: theses
Subject:: Applied mathematics; Statistics; Biostatistics; Survival Analysis; Asymptotic Theory; Nonparametric Statistics; Missing Data; Censored Data; Mathematical Statistics; Event History Analysis; Estimation Theory; Mathematics; Simulations; Medical Statistics
DOI: https://doi.org/10.26300/j446-av83

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Abstract:: We extend the results presented by Antos et al. [1] for nonparametric estimation methods using complete datasets to nonparametric regression estimators that use right censored (incomplete) datasets. Specifically, we establish novel asymptotic least upper error bounds for the estimators first constructed by Buckley and James [6], Koul et al. [7], and Rubin and van der Laan. [4] Moreover, we prove two corollaries that follow from our results under the Dedekind-MacNeille completion of the real numbers. [8] We then discuss the significance of these error bounds, as well as their limitations and the impact of the assumptions under which they hold. Additionally, we run simulations for all three estimators, which provide some practical support to our theoretical results. Finally, we comment on the mathematical limitations of our theoretical results and the computational limitations of our simulations, pointing out areas of improvement and potential future research avenues.
Notes:: Senior thesis (ScB)--Brown University, 2023; Concentration: Statistics

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Provost, Nathan Thomas, "Asymptotic Error Bounds for Nonparametric Censoring Unbiased Estimators of Restricted Mean Survival Times" (2023). Biostatistics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://doi.org/10.26300/j446-av83

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Biostatistics Theses and Dissertations

Theses and Dissertations for the Biostatistics department.
...

Asymptotic Error Bounds for Nonparametric Censoring Unbiased Estimators of Restricted Mean Survival Times