Fernández, T;
Rivera, N;
(2020)
Kaplan-Meier V- and U-statistics.
Electronic Journal of Statistics
, 14
(1)
pp. 1872-1916.
10.1214/20-ejs1704.
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Abstract
In this paper, we study Kaplan-Meier V- and U-statistics respectively defined as \theta (\widehat{F}_{n})=\sum _{i,j}K(X_{[i:n]},X_{[j:n]})W_{i}W_{j} and \theta _{U}(\widehat{F}_{n})=\sum _{i\neq j}K(X_{[i:n]},X_{[j:n]})W_{i}W_{j}/\sum _{i\neq j}W_{i}W_{j}, where \widehat{F}_{n} is the Kaplan-Meier estimator, \{W_{1},\ldots ,W_{n}\} are the Kaplan-Meier weights and K:(0,\infty )^{2}\to \mathbb{R} is a symmetric kernel. As in the canonical setting of uncensored data, we differentiate between two asymptotic behaviours for \theta (\widehat{F}_{n}) and \theta _{U}(\widehat{F}_{n}). Additionally, we derive an asymptotic canonical V-statistic representation of the Kaplan-Meier V- and U-statistics. By using this representation we study properties of the asymptotic distribution. Applications to hypothesis testing are given.
| Type: | Article |
|---|---|
| Title: | Kaplan-Meier V- and U-statistics |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/20-ejs1704 |
| Publisher version: | https://doi.org/10.1214/20-ejs1704 |
| Language: | English |
| Additional information: | © 2020 The Authors. Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Kaplan-Meier estimator, right-censoring, Vstatistics |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences > Gatsby Computational Neurosci Unit |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10096152 |
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