TY - JOUR
T1 - Kaplan-meier v-and u-statistics
AU - Fernández, Tamara
AU - Rivera, Nicolás
N1 - Funding Information:
Tamara Fernández was supported by the Biometrika Trust. Nicolás Rivera was supported by Thomas Sauerwald’s ERC Starting Grant 679660 DYNAMIC MARCH.
Funding Information:
Tamara Fern?ndez was supported by the Biometrika Trust. Nicol?s Rivera was supported by Thomas Sauerwald?s ERC Starting Grant 679660 DYNAMIC MARCH.
Publisher Copyright:
© 2020, Institute of Mathematical Statistics. All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Kaplan-Meier estimator
KW - Right-censoring
KW - V-statistics
UR - http://www.scopus.com/inward/record.url?scp=85088927740&partnerID=8YFLogxK
U2 - 10.1214/20-EJS1704
DO - 10.1214/20-EJS1704
M3 - Article
AN - SCOPUS:85088927740
VL - 14
SP - 1872
EP - 1916
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
IS - 1
ER -