Kaplan-meier v-and u-statistics

Tamara Fernández; Nicolás Rivera

doi:10.1214/20-EJS1704

Kaplan-meier v-and u-statistics

Tamara Fernández, Nicolás Rivera

Resultado de la investigación: Contribución a una revista › Artículo › revisión exhaustiva

3 Citas (Scopus)

Resumen

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])WⁱW^j and θ^U (̂Fⁿ)=_i≠j K(X_[i:n],X_[j:n])W_iW_j /_i≠j W_iW_j,where ̂F_n is the Kaplan-Meier estimator, {W₁,…,W_n} 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(̂F_n)andθ_U (̂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.

Idioma original	Inglés
Páginas (desde-hasta)	1872-1916
Número de páginas	45
Publicación	Electronic Journal of Statistics
Volumen	14
N.º	1
DOI	https://doi.org/10.1214/20-EJS1704
Estado	Publicada - 2020
Publicado de forma externa	Sí

Acceder al documento

10.1214/20-EJS1704

Citar esto

@article{9ce46b6e84f449f2a7c6aaa9e315f8f8,

title = "Kaplan-meier v-and u-statistics",

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.",

keywords = "Kaplan-Meier estimator, Right-censoring, V-statistics",

author = "Tamara Fern{\'a}ndez and Nicol{\'a}s Rivera",

note = "Funding Information: Tamara Fern{\'a}ndez was supported by the Biometrika Trust. Nicol{\'a}s Rivera was supported by Thomas Sauerwald{\textquoteright}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: {\textcopyright} 2020, Institute of Mathematical Statistics. All rights reserved.",

year = "2020",

doi = "10.1214/20-EJS1704",

language = "English",

volume = "14",

pages = "1872--1916",

journal = "Electronic Journal of Statistics",

issn = "1935-7524",

number = "1",

}

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 -

Kaplan-meier v-and u-statistics

Resumen

Acceder al documento

Huella

Citar esto