On estimated projection pursuit-type Crámer-Von Mises statistics

Lixing Zhu; Kai Tai Fang; M. Ishaq Bhatti

doi:10.1006/jmva.1997.1673

On estimated projection pursuit-type Crámer-Von Mises statistics

Lixing Zhu^*, Kai Tai Fang, M. Ishaq Bhatti

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

12 Citations (Scopus)

Abstract

This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Crámer-Von Mises-type test statistics are constructed using projection pursuit technique. Some interested properties of the test statistics, like asymptotics, bootstrap approximations, and the tail behavior of the limits of test statistics are investigated. For computational reasons, an approximation via the number theoretic method to the extreme value and the integral on a super sphere surface is considered.

Original language	English
Pages (from-to)	1-14
Number of pages	14
Journal	Journal of Multivariate Analysis
Volume	63
Issue number	1
DOIs	https://doi.org/10.1006/jmva.1997.1673
Publication status	Published - Oct 1997

Scopus Subject Areas

Statistics and Probability
Numerical Analysis
Statistics, Probability and Uncertainty

User-Defined Keywords

Bootstrap
Number-theoretic method
Projection pursuit
Tail probability

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10.1006/jmva.1997.1673

Cite this

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title = "On estimated projection pursuit-type Cr{\'a}mer-Von Mises statistics",

abstract = "This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Cr{\'a}mer-Von Mises-type test statistics are constructed using projection pursuit technique. Some interested properties of the test statistics, like asymptotics, bootstrap approximations, and the tail behavior of the limits of test statistics are investigated. For computational reasons, an approximation via the number theoretic method to the extreme value and the integral on a super sphere surface is considered.",

keywords = "Bootstrap, Number-theoretic method, Projection pursuit, Tail probability",

author = "Lixing Zhu and Fang, {Kai Tai} and Bhatti, {M. Ishaq}",

note = "Funding Information: Supported by a Hong Kong UPGC grant, the NNSF of China and the URIS of Griffith University, Australia. Part of this research was done when the first author was visiting Institut de Statistique, Catholique University Louvain, Belgium. Research support from the contract {\textquoteleft}{\textquoteleft}Projet d{\textquoteright}Actions de Recherche Concertees{\textquoteright}{\textquoteright} (PARC No. 93/98-164) of the Belgian Government is gratefully acknowledged.",

year = "1997",

month = oct,

doi = "10.1006/jmva.1997.1673",

language = "English",

volume = "63",

pages = "1--14",

journal = "Journal of Multivariate Analysis",

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T1 - On estimated projection pursuit-type Crámer-Von Mises statistics

AU - Zhu, Lixing

AU - Fang, Kai Tai

AU - Bhatti, M. Ishaq

N1 - Funding Information: Supported by a Hong Kong UPGC grant, the NNSF of China and the URIS of Griffith University, Australia. Part of this research was done when the first author was visiting Institut de Statistique, Catholique University Louvain, Belgium. Research support from the contract ‘‘Projet d’Actions de Recherche Concertees’’ (PARC No. 93/98-164) of the Belgian Government is gratefully acknowledged.

PY - 1997/10

Y1 - 1997/10

N2 - This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Crámer-Von Mises-type test statistics are constructed using projection pursuit technique. Some interested properties of the test statistics, like asymptotics, bootstrap approximations, and the tail behavior of the limits of test statistics are investigated. For computational reasons, an approximation via the number theoretic method to the extreme value and the integral on a super sphere surface is considered.

AB - This paper addresses the problem of testing for a multivariate distribution, which belongs to a known parametric distribution family. The estimated Crámer-Von Mises-type test statistics are constructed using projection pursuit technique. Some interested properties of the test statistics, like asymptotics, bootstrap approximations, and the tail behavior of the limits of test statistics are investigated. For computational reasons, an approximation via the number theoretic method to the extreme value and the integral on a super sphere surface is considered.

KW - Bootstrap

KW - Number-theoretic method

KW - Projection pursuit

KW - Tail probability

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U2 - 10.1006/jmva.1997.1673

DO - 10.1006/jmva.1997.1673

M3 - Journal article

AN - SCOPUS:0031256799

SN - 0047-259X

VL - 63

SP - 1

EP - 14

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

IS - 1

ER -

On estimated projection pursuit-type Crámer-Von Mises statistics

Abstract

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