Third-order local power properties of tests for a composite hypothesis

Yoshihide Kakizawa

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 303-317

Abstract: This paper addresses, for a composite hypothesis about a subvector of the parameters in the parametric model, the issues posed by Rao and Mukerjee (1995) [22] and Li (2001) [14] on the power under a sequence of local alternatives. It is shown that a partially adjusted test statistic in a class of test statistics is equally sensitive (up to the third-order) to the change of the nuisance parameters. However, there exist infinitely many ways for improving the chi-squared approximation to the null distribution, which reveal, in general, the non-equivalence of the resulting third-order point-by-point local powers. To make a definitive conclusion, the average local power is then considered, from which the third-order asymptotic optimality of the Bartlett-type adjusted Rao test can be also established.

Keywords: Asymptotic expansion; Bartlett-type adjustment; Local alternative; Local power of test; Nuisance parameter; Sensitivity analysis (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2012.08.009

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