Kaplan-meier v-and u-statistics

Tamara Fernández, Nicolás Rivera

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this paper, we study∑ Kaplan-Meier V-and U-statistics re-spectively ∑ defined as θ(̂Fn)=∑i,j K(X[i:n],X[j:n])WiWj and θU (̂Fn)=i≠j K(X[i:n],X[j:n])WiWj /i≠j WiWj,where ̂Fn is the Kaplan-Meier estimator, {W1,…,Wn} are the Kaplan-Meier weights and K:(0, ∞)2 → R is a symmetric kernel. As in the canonical setting of uncensored data, we differentiate between two asymptotic behaviours for θ(̂Fn)andθU (̂Fn). 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.

Original languageEnglish
Pages (from-to)1872-1916
Number of pages45
JournalElectronic Journal of Statistics
Volume14
Issue number1
DOIs
StatePublished - 2020
Externally publishedYes

Keywords

  • Kaplan-Meier estimator
  • Right-censoring
  • V-statistics

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