Asymptotic approximations for the distributions of multinomial goodness-of-fit statistics

Siotani, Minoru; Fujikoshi, Yasunori

doi:10.32917/hmj/1206133150

Cited by 42 publications

(29 citation statements)

References 4 publications

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“…Siotani and Fujikoshi in [17] applied Yarnold's approach not only to Pearson's chi-square statistic but to log-likelihood ratio and Freeman-Tukey statistics as well. In the case of last two statistics the corresponding set B is not exactly an ellipsoid but only "approximated" by ellipsoid.…”

Section: Introduction and Main Resultsmentioning

confidence: 98%

Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

Bogatyrev

Götze

Ulyanov

2006

Journal of Multivariate Analysis

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We consider short asymptotic expansions for the probability of a sum of i.i.d. random elements to hit a ball in a Hilbert space H. The error bound for the expansion is of order O(n −1 ). It depends on the first 12 eigenvalues of the covariance operator only. Moreover, the bound is non-uniform, i.e. the accuracy of the approximation becomes better as the distance between a boundary of the ball and the origin in H grows.

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Section: Introduction and Main Resultsmentioning

confidence: 98%

Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

Bogatyrev

Götze

Ulyanov

2006

Journal of Multivariate Analysis

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“…For some of these studies, see Fujikosih and Isogai [43], Fujikoshi and Ochi [53], Siotani and Fujikoshi [99], Fujikoshi and Nishii [50], Fujikoshi et al [48], Kariya et al [80], Fujikoshi and Watamori [64], Otake et al [86], Fujikoshi [31], Seo et al [96], Naito et al [85], Kanda and Fujikoshi [77], Gupta et al [68], etc. At the time of his retirement of Hiroshima University, the number of published papers written by Professor Fujikoshi was 124, and after retirement, he has written another eight papers.…”

Section: Discussionmentioning

confidence: 96%

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Siotani

Wakaki

2006

Journal of Multivariate Analysis

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The purpose of this article is to review the findings of Professor Fujikoshi which are primarily in multivariate analysis. He derived many asymptotic expansions for multivariate statistics which include MANOVA tests, dimensionality tests and latent roots under normality and nonnormality. He has made a large contribution in the study on theoretical accuracy for asymptotic expansions by deriving explicit error bounds. A large contribution has been also made in an important problem involving the selection of variables with introducing "no additional information hypotheses" in some multivariate models and the application of model selection criteria. Recently he is challenging to a high-dimensional statistical problem. He has been involved in other topics in multivariate analysis, such as power comparison of a class of tests, monotone transformations with improved approximations, etc.

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“…The Edgeworth expansion for the distribution of the statistic G2(Y) can be expressed as Here we note that for aj = 0 for all j and c = 0 in (2.4), we obtain the result (4.8) obtained by Siotani and Fujikoshi (1984). In practice, we add the same constant, say a, to every cell i.e., aj = a for all j to smooth G 2.…”

Section: Modified Likelihood Ratio Statisticmentioning

confidence: 99%

Smoothing of likelihood ratio statistic for equiprobable multinomial goodness-of-fit

Hosmane

1990

Ann Inst Stat Math

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Asymptotic approximations for the distributions of multinomial goodness-of-fit statistics

Cited by 42 publications

References 4 publications

Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Smoothing of likelihood ratio statistic for equiprobable multinomial goodness-of-fit

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