Testing multivariate uniformity and its applications
Liang, JJ; Fang, KT; Hickernell, FJ; Li, RZ
AbstractSome new Statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1](d) (d greater than or equal to 2). These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in [0, 1](d). Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in [0, 1](d)., obtain some asymptotic properties of the new statistics. By Monte Carlo simulation, it is found that the finite-sample distributions of the new statistics are well approximated by the standard normal distribution, N(0, 1), or the chi-squared distribution, chi (2)(2). A power study is performed, and possible applications of the new statistics to testing general multivariate goodness-of-fit problems are discussed.
Keywordgoodness-of-fit discrepancy quasi-Monte Carlo methods testing uniformity
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000166514000018
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Document Type期刊论文
Corresponding AuthorLiang, JJ
Affiliation1.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
2.Chinese Acad Sci, Inst Appl Math, Beijing, Peoples R China
3.Univ N Carolina, Dept Stat, Chapel Hill, NC 27599 USA
Recommended Citation
GB/T 7714
Liang, JJ,Fang, KT,Hickernell, FJ,et al. Testing multivariate uniformity and its applications[J]. MATHEMATICS OF COMPUTATION,2001,70(233):337-355.
APA Liang, JJ,Fang, KT,Hickernell, FJ,&Li, RZ.(2001).Testing multivariate uniformity and its applications.MATHEMATICS OF COMPUTATION,70(233),337-355.
MLA Liang, JJ,et al."Testing multivariate uniformity and its applications".MATHEMATICS OF COMPUTATION 70.233(2001):337-355.
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