On a new approach to the multi-sample goodness-of-fit problem

Research output: Contribution to journalArticleResearch

Authors

  • Daniel Gaigall
View graph of relations

Details

Original languageEnglish
Pages (from-to)2971-2989
Number of pages19
JournalCommunications in Statistics Part B: Simulation and Computation
Volume50
Issue number10
Publication statusPublished - 22 May 2019

Abstract

Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.

Keywords

    Goodness-of-fit test, Multi-sample problem, Parametric bootstrap

ASJC Scopus subject areas

Cite this

On a new approach to the multi-sample goodness-of-fit problem. / Gaigall, Daniel.
In: Communications in Statistics Part B: Simulation and Computation, Vol. 50, No. 10, 22.05.2019, p. 2971-2989.

Research output: Contribution to journalArticleResearch

Download
@article{76313d1bff264fed9f80412aa72b18ac,
title = "On a new approach to the multi-sample goodness-of-fit problem",
abstract = "Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions. ",
keywords = "Goodness-of-fit test, Multi-sample problem, Parametric bootstrap",
author = "Daniel Gaigall",
note = "Publisher Copyright: {\textcopyright} 2019, {\textcopyright} 2019 Taylor & Francis Group, LLC.",
year = "2019",
month = may,
day = "22",
doi = "10.1080/03610918.2019.1618472",
language = "English",
volume = "50",
pages = "2971--2989",
journal = "Communications in Statistics Part B: Simulation and Computation",
issn = "0361-0918",
publisher = "Taylor and Francis Ltd.",
number = "10",

}

Download

TY - JOUR

T1 - On a new approach to the multi-sample goodness-of-fit problem

AU - Gaigall, Daniel

N1 - Publisher Copyright: © 2019, © 2019 Taylor & Francis Group, LLC.

PY - 2019/5/22

Y1 - 2019/5/22

N2 - Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.

AB - Suppose we have k samples X 1,1..,X 1,n1..,X k,1..,X k,nk with different sample sizes n 1,...,n k and unknown underlying distribution functions F 1,...,F k as observations plus k families of distribution functions (Formula presented.) each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not F 1,...,F k belongs to the parametric family (Formula presented.) New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.

KW - Goodness-of-fit test

KW - Multi-sample problem

KW - Parametric bootstrap

UR - http://www.scopus.com/inward/record.url?scp=85066886364&partnerID=8YFLogxK

U2 - 10.1080/03610918.2019.1618472

DO - 10.1080/03610918.2019.1618472

M3 - Article

VL - 50

SP - 2971

EP - 2989

JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

SN - 0361-0918

IS - 10

ER -