Asymptotic expansions for a class of tests for a general covariance structure under a local alternative
| Autor: | Hirofumi Wakaki, Hiroaki Shimizu |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Wishart distribution
Statistics and Probability Class (set theory) Numerical Analysis Mauchly's sphericity test Asymptotic expansion Covariance Non-null distribution Local alternative Combinatorics Sphericity test Distribution (mathematics) Linear structure Power comparison Class of test statistics Statistics Probability and Uncertainty General covariance structure Random matrix Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Multivariate Analysis. 102(6):1080-1089 |
| ISSN: | 0047-259X |
| DOI: | 10.1016/j.jmva.2011.03.002 |
| Popis: | Let S be a pxp random matrix having a Wishart distribution W"p(n,n^-^1@S). For testing a general covariance structure @S=@S(@x), we consider a class of test statistics T"h=n@r"h(S,@S(@x@?)), where @r"h(@S"1,@S"2)=@?"i"="1^ph(@l"i) is a distance measure from @S"1 to @S"2, @l"i's are the eigenvalues of @S"1@S"2^-^1, and h is a given function with certain properties. Wakaki, Eguchi and Fujikoshi (1990) suggested this class and gave an asymptotic expansion of the null distribution of T"h. This paper gives an asymptotic expansion of the non-null distribution of T"h under a sequence of alternatives. By using results, we derive the power, and compare the power asymptotically in the class. In particular, we investigate the power of the sphericity tests. |
| Databáze: | OpenAIRE |
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