Higher-order Bartlett-type adjustment |
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| Institution: | 1. School of Statistics, JiangXi University of Finance and Economics, Nanchang, JiangXi 330013, China;2. Applied Statistics Research Center, Nanchang, Jiangxi 330013, China;1. School of Management, Hefei University of Technology, Hefei 230009, China;2. Key Laboratory of Process Optimization and Intelligent Decision-Making (Hefei University of Technology), Ministry of Education, Hefei 230009, China;3. China Institute of Water Resources and Hydropower Research, Beijing 100048, China |
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| Abstract: | This paper deals with Bartlett-type adjustment which makes all the terms up to order n−k in the asymptotic expansion vanish, where k is an integer k ⩾ 1 and n depends on the sample size. Extending Cordeiro and Ferrari (1991, Biometrika, 78, 573–582) for the case of k = 1, we derive a general formula of the kth-order Bartlett-type adjustment for the test statistic whose kth-order asymptotic expansion of the distribution is given by a finite linear combination of chi-squared distribution with suitable degrees of freedom. Two examples of the second-order Bartlett-type adjustment are given. We also elucidate the connection between Bartlett-type adjustment and Cornish-Fisher expansion. |
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