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January 2006 Transformations with improved asymptotic approximations and their accuracy
Hiroyuki Enoki, Makoto Aoshima
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SUT J. Math. 42(1): 97-122 (January 2006). DOI: 10.55937/sut/1159987680


Suppose that a statistic S is asymptotically distributed as a distribution function G(x) as some parameter ϵ0. We consider monotone transformations of S in order to improve the asymptotic approximation. The transformations proposed here preserve monotonicity and give transformed statistics T(S) whose distribution function is coincident with G(x) up to the order O(ϵr1). It may be observed that the proposed transformations give a significant improvement to approximations. Further, we shall also consider error bounds for the remainder term of an asymptotic expansion for the distribution of T(S). Finally, some applications of the findings are demonstrated for some test statistics.

Funding Statement

Research of the second author was partially supported by Grant-in-Aid for Exploratory Research, the Ministry of Education, Culture, Sports, Science and Technology, Japan, under Contract Number 16650059.


We are grateful to the referee for helpful comments.


Download Citation

Hiroyuki Enoki. Makoto Aoshima. "Transformations with improved asymptotic approximations and their accuracy." SUT J. Math. 42 (1) 97 - 122, January 2006.


Received: 11 January 2006; Revised: 27 June 2006; Published: January 2006
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1159987680

Primary: 62E20

Keywords: asymptotic expansion , Bartlett type correction , error bound , transformation

Rights: Copyright © 2006 Tokyo University of Science

Vol.42 • No. 1 • January 2006
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