Higher Order Approximations to a Percentage Point

Masafumi Akahira ()
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Masafumi Akahira: Uninversity of Tsukuba, Professor Emeritus

Chapter Chapter 10 in Theory of Statistical Estimation, 2026, pp 279-330 from Springer

Abstract: Abstract A higher order approximation formula for a percentage point of the noncentral t-distribution with ν $$\nu $$ degrees of freedom is given up to the order o ( ν −3 ) $$o(\nu ^{-3})$$ under the normality assumption, using the Cornish-Fisher expansion for the statistic based on a linear combination of a normal random variable and a chi-random variable. The upper confidence limit and the confidence interval for the noncentrality parameter are given. Although the approximation formula is represented as a solution of the equation, its existence and uniqueness are shown to be guaranteed. In a similar way to the above, without the normality assumption, a higher order approximation formula to a percentage point of the distribution of the noncentral t-statistic is also given. Further, a higher order approximation formula for a percentage point of the distribution of the sample correlation coefficient is given up to the order O ( n −1 ) $$O(n^{-1})$$ with a size n of sample. Numerical results are also given.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-95-5339-6_10

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DOI: 10.1007/978-981-95-5339-6_10

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