Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data

Publikation: Beitrag in FachzeitschriftArtikelForschung

Autoren

  • Daniel Gaigall
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)437 - 465
Seitenumfang29
FachzeitschriftMetrika
Jahrgang83
Ausgabenummer4
Frühes Online-Datum3 Sept. 2019
PublikationsstatusVeröffentlicht - Mai 2020

Abstract

We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.

ASJC Scopus Sachgebiete

Zitieren

Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data. / Gaigall, Daniel.
in: Metrika, Jahrgang 83, Nr. 4, 05.2020, S. 437 - 465.

Publikation: Beitrag in FachzeitschriftArtikelForschung

Gaigall D. Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data. Metrika. 2020 Mai;83(4):437 - 465. Epub 2019 Sep 3. doi: 10.1007/s00184-019-00742-5
Download
@article{c031739ed3084f4db9c526e6239dff5c,
title = "Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data",
abstract = "We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Cr{\'a}mer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.",
keywords = "Cr{\'a}mer–von-Mises distance, Incomplete data, Marginal homogeneity test, Paired sample, Resampling test",
author = "Daniel Gaigall",
year = "2020",
month = may,
doi = "10.1007/s00184-019-00742-5",
language = "English",
volume = "83",
pages = "437 -- 465",
journal = "Metrika",
issn = "0026-1335",
publisher = "Springer Verlag",
number = "4",

}

Download

TY - JOUR

T1 - Testing marginal homogeneity of a continuous bivariate distribution with possibly incomplete paired data

AU - Gaigall, Daniel

PY - 2020/5

Y1 - 2020/5

N2 - We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.

AB - We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.

KW - Crámer–von-Mises distance

KW - Incomplete data

KW - Marginal homogeneity test

KW - Paired sample

KW - Resampling test

UR - http://www.scopus.com/inward/record.url?scp=85072110453&partnerID=8YFLogxK

U2 - 10.1007/s00184-019-00742-5

DO - 10.1007/s00184-019-00742-5

M3 - Article

VL - 83

SP - 437

EP - 465

JO - Metrika

JF - Metrika

SN - 0026-1335

IS - 4

ER -