Asymptotic Results on a General Class of Empirical Statistics: Power and Confidence Interval Properties

Chang, In Hong; Mukerjee, Rahul

doi:10.1007/s10463-006-0040-1

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…The above-mentioned papers were concerned only with the null distribution. In line with Chen [33], Bravo [34], Mukerjee [35] and Chang and Mukerjee [36] for the third-order local power analyses, our arguments could be applied to the ED test statistic including the more general case of over-determined moment based models. The calculations involved in this case would, however, be extremely difficult.…”

Section: Resultsmentioning

confidence: 62%

Comparison of Bartlett-type adjusted tests in the multiparameter case

Kakizawa

2010

Journal of Multivariate Analysis

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a b s t r a c tConsidering some Bartlett-type adjusted tests for a simple hypothesis about a multidimensional parameter, this paper clarifies similarities and dissimilarities with the oneparameter case developed in the 1990s, where a major emphasis is put on the issue posed by Rao and Mukerjee [C.R. Rao, R. Mukerjee, Comparison of Bartlett-type adjustments for the efficient score statistic, J. Statist. Plann. Inference 46 (1995) 137-146] on the power under a sequence of local alternatives. Not surprisingly, there is an infinite number of adjustments which extend Chandra-Mukerjee and Taniguchi approaches to the multiparameter case. Revisiting their ideas, this paper presents four specific cases (type K , K = 0, 1, 2, 3) and gives a sufficient condition under which our generalized adjustment for each case is uniquely determined, where type 0 is a counterpart of Chandra and Mukerjee's original proposal for Rao's test statistic, whereas the latter three types are introduced as double adjustments related to the Cordeiro and Ferrari approach. If the adjustment of type 1 is made instead of type K , K = 0, 2, 3, it is shown that Chandra and Mukerjee's approach is equivalent to Taniguchi's approach in terms of the third-order local power. The same is partially true for type 0, depending on the model under consideration. However, the adjustments of type K , K = 2, 3, reveal, in general, the non-equivalence of these two approaches in terms of the third-order local power.

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Section: Resultsmentioning

confidence: 62%

Comparison of Bartlett-type adjusted tests in the multiparameter case

Kakizawa

2010

Journal of Multivariate Analysis

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show abstract

“…Also, let a i0 = a i (β 3 ), a i0 = a i (β 3 ), b i0 = b i (β 3 , β 4 ). Observe that u in (6) has the same form as in (2) of Chang and Mukerjee (2006), ourỹ being the same as their y. Hence, following Sect.…”

Section: Confidence Intervalmentioning

confidence: 91%

“…4 of Chang and Mukerjee (2006). However, we still retained the intermediate steps indicated in the previous paragraph because such substitution also involves considerable algebra and, more importantly, the Edgeworth expansion in (8) will be required later in Sect.…”

Section: Confidence Intervalmentioning

confidence: 99%