Improved chi-squared tests for a composite hypothesis

Yoshihide Kakizawa

Journal of Multivariate Analysis, 2012, vol. 107, issue C, 141-161

Abstract: The Bartlett-type adjustment is a higher-order asymptotic method for improving the chi-squared approximation to the null distributions of various test statistics. Though three influential papers were published in 1991—Chandra and Mukerjee (1991) [8], Cordeiro and Ferrari (1991) [12] and Taniguchi (1991) [36] in alphabetical order, the only CF-approach has been frequently applied in the literature during the last two decades, provided that asymptotic expansion for the null distribution of a given test statistic is available. Revisiting the CM/T-approaches developed in the absence of a nuisance parameter, this paper suggests general adjustments for a class of test statistics that includes, in particular, the likelihood ratio, Rao’s and Wald’s test statistics in the presence of a nuisance parameter.

Keywords: Asymptotic expansion; Bartlett-type adjustment; Chi-squared approximation; Composite hypothesis; Nuisance parameter (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.jmva.2012.01.008

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