Asymptotic normality of quadratic forms with random vectors of increasing dimension

dc.contributor.authorPeng, Hanxiang
dc.contributor.authorSchick, Anton
dc.contributor.departmentMathematical Sciences, School of Scienceen_US
dc.date.accessioned2017-12-28T17:02:06Z
dc.date.available2017-12-28T17:02:06Z
dc.date.issued2018-03
dc.description.abstractThis paper provides sufficient conditions for the asymptotic normality of quadratic forms of averages of random vectors of increasing dimension and improves on conditions found in the literature. Such results are needed in applications of Owen’s empirical likelihood when the number of constraints is allowed to grow with the sample size. Indeed, the results of this paper are already used in Peng and Schick (2013) for this purpose. We also demonstrate how our results can be used to obtain the asymptotic distribution of the empirical likelihood with an increasing number of constraints under contiguous alternatives. In addition, we discuss potential applications of our result. The first example focuses on a chi-square test with an increasing number of cells. The second example treats testing for the equality of the marginal distributions of a bivariate random vector. The third example generalizes a result of Schott (2005) by showing that a standardized version of his test for diagonality of the dispersion matrix of a normal random vector is asymptotically standard normal even if the dimension increases faster than the sample size. Schott’s result requires the dimension and the sample size to be of the same order.en_US
dc.eprint.versionAuthor's manuscripten_US
dc.identifier.citationPeng, H., & Schick, A. (2018). Asymptotic normality of quadratic forms with random vectors of increasing dimension. Journal of Multivariate Analysis. https://doi.org/10.1016/j.jmva.2017.11.002en_US
dc.identifier.urihttps://hdl.handle.net/1805/14907
dc.language.isoenen_US
dc.publisherElsevieren_US
dc.relation.isversionof10.1016/j.jmva.2017.11.002en_US
dc.relation.journalJournal of Multivariate Analysisen_US
dc.rightsPublisher Policyen_US
dc.sourceAuthoren_US
dc.subjectChi-square test with increasing number of cellsen_US
dc.subjectempirical likelihooden_US
dc.subjectequal marginalsen_US
dc.titleAsymptotic normality of quadratic forms with random vectors of increasing dimensionen_US
dc.typeArticleen_US
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