Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system

Fujikoshi, Yasunori; Morimune, Kimio; Kunitomo, Naoto; Taniguchi, Masanobu

doi:10.1016/0304-4076(82)90035-5

Cited by 30 publications

(25 citation statements)

References 7 publications

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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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Section: Discussionmentioning

confidence: 96%

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Siotani

Wakaki

2006

Journal of Multivariate Analysis

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“…Our method is the conditional expansion approach, which is similar to the one in Fujikoshi et al [17] and Anderson et al [4]. Because the early works could utilize aspects of the multivariate normal distributions directly which we cannot use, the derivations of asymptotic expansions become more complicated, as explained in Appendix A.…”

Section: The Methods Of Asymptotic Expansions and Assumptionsmentioning

confidence: 98%

“…Our formulation and method are intentionally similar to the earlier studies on the single equation estimation methods by Fujikoshi et al [17] and Anderson et al [4]. It is mainly because useful interpretations can be drawn in the light of past studies on the finite sample properties of estimators in the classical parametric framework as well as in the semi-parametric framework.…”

Section: Introductionmentioning

confidence: 95%

Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations

Kunitomo

Matsushita

2009

Journal of Multivariate Analysis

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a b s t r a c t Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous equations, which corresponds to a reduced rank regression model. The expansions in terms of the sample size, when the noncentrality parameters increase proportionally, are carried out to O(n −1 ). Comparisons of the distributions of the MEL and GMM estimators are made. Also, we relate the asymptotic expansions of the distributions of the MEL and GMM estimators to the corresponding expansions for the Limited Information Maximum Likelihood (LIML) and the Two-Stage Least Squares (TSLS) estimators. We give useful information on the higher order properties of alternative estimators including the semi-parametric inefficiency factor under the homoscedasticity assumption.

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“…The discussion of validity of formal expansions is omitted to save space, but it can be obtained by following arguments given by Anderson [2] and Fujikoshi et al [8]. The next lemma, which plays a key role in later development, is similar to Theorem 3 in Morimune and Kunitomo [16].…”

Section: V* = Rp(--~x + Y)/(a(1 § #~)Ln) = (V 9 9 V~ 0) Where E(umentioning

confidence: 93%

“…We note that in their derivation the asymptotic variance formula (A. 8) can be rewritten as AV(~)=2((1+~2)r which is minimized when the first part is zero. where r (i=1, 2,3) evaluated at h,=s~=l+# 2, h~=s~=#p and h3=s~= l + p. …”

Section: V* = Rp(--~x + Y)/(a(1 § #~)Ln) = (V 9 9 V~ 0) Where E(umentioning

confidence: 99%

A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics

Kunitomo

1987

Ann Inst Stat Math

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SummaryThe maximum likelihood (ML) estimator and its modification in the linear functional relationship model with incidental parameters are shown to be third-order asymptotically efficient among a class of almost medianunbiased and almost mean-unbiased estimators, respectively, in the large sample sense. This means that the limited information maximum likelihood (LIML) estimator in the simultaneous equation system is thirdorder asymptotically efficient when the number of excluded exogenous ~ variables in a particular structural equation is growing along with the sample size. It implies that the LIML estimator has an optimum property when the system of structural equations is large.

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Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system

Cited by 30 publications

References 7 publications

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Contributions to multivariate analysis by Professor Yasunori Fujikoshi

Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations

A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics

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