Author
Tatsuya Kubokawa
Other affiliations: University of Tsukuba, University of Rouen
Bio: Tatsuya Kubokawa is an academic researcher from University of Tokyo. The author has contributed to research in topics: Estimator & Small area estimation. The author has an hindex of 22, co-authored 248 publications receiving 1986 citations. Previous affiliations of Tatsuya Kubokawa include University of Tsukuba & University of Rouen.
Papers published on a yearly basis
Papers
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TL;DR: In this article, the point and interval estimation of the variance of a normal distribution with an unknown mean was studied and the best affine equivariant estimators were derived by Stein's truncated and Brewster and Zidek's smooth procedures.
Abstract: In the point and interval estimation of the variance of a normal distribution with an unknown mean, the best affine equivariant estimators are dominated by Stein's truncated and Brewster and Zidek's smooth procedures, which are separately derived. This paper gives a unified approach to this problem by using a simple definite integral and provides a class of improved procedures in both point and interval estimation of powers of the scale parameter of normal, lognormal, exponential and Pareto distributions. Finally, the same method is applied to the improvement on the James-Stein rule in the simultaneous estimation of a multinormal mean.
130 citations
TL;DR: In this article, the Stein-Haff identity is established for a singular Wishart distribution with a positive definite mean matrix but with the dimension larger than the degrees of freedom, and the precision estimators are used in a quadratic discriminant rule, and it is shown through simulation that discriminant methods based on the ridge-type empirical Bayes estimators provide higher correct classification rates.
66 citations
TL;DR: This article considers the problem of testing the equality of mean vectors of dimension p of several groups with a common unknown non-singular covariance matrix @S, based on N independent observation vectors where N may be less than the dimension p and proposes a test that has the above invariance property.
58 citations
TL;DR: Tests are proposed for sphericity and for testing the hypothesis that the covariance matrix @S is an identity matrix, by providing an unbiased estimator of tr[@S^2] under the general model which requires no more computing time than the one available in the literature for a normal model.
56 citations
TL;DR: In this paper, the authors show that minimax and shrinkage estimators under a normal distribution remain robust under an elliptically contoured distribution for both invariant and non-invariant loss functions in a multivariate linear regression model.
54 citations
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1,677 citations
Book•
19 Jun 2002TL;DR: In this article, the Multivariate Normal Distribution, Multivariate Normality, and Covariance Structure were used for one-and two-sample tests to compare the performance of vector and matrix algebra.
Abstract: Introduction.- Vector and Matrix Algebra.- The Multivariate Normal Distribution, Multivariate Normality, and Covariance Structure.- One- and Two-Sample Tests.- Multivariate Analysis of Variance.- Discriminant Analysis.- Canonical Correlation.- Principal Component Analysis.- Factor Analysis.- Structural Equations.
651 citations
TL;DR: The authors analytically derived the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio and showed that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance.
Abstract: In this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical results show that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.
610 citations
25 Jun 2004
TL;DR: In this paper, a nonlinear version of the Gauss-Markov Theorem is used for estimating the risk matrix of a least square estimator in a two-equation Heteroscedastic model.
Abstract: Preface.1 Preliminaries.1.1 Overview.1.2 Multivariate Normal and Wishart Distributions.1.3 Elliptically Symmetric Distributions.1.4 Group Invariance.1.5 Problems.2 Generalized Least Squares Estimators.2.1 Overview.2.2 General Linear Regression Model.2.3 Generalized Least Squares Estimators.2.4 Finiteness of Moments and Typical GLSEs.2.5 Empirical Example: CO2 Emission Data.2.6 Empirical Example: Bond Price Data.2.7 Problems.3 Nonlinear Versions of the Gauss-Markov Theorem.3.1 Overview.3.2 Generalized Least Squares Predictors.3.3 A Nonlinear Version of the Gauss-Markov Theorem in Prediction.3.4 A Nonlinear Version of the Gauss-Markov Theorem in Estimation.3.5 An Application to GLSEs with Iterated Residuals.3.6 Problems.4 SUR and Heteroscedastic Models.4.1 Overview.4.2 GLSEs with a Simple Covariance Structure.4.3 Upper Bound for the Covariance Matrix of a GLSE.4.4 Upper Bound Problem for the UZE in an SUR Model.4.5 Upper Bound Problems for a GLSE in a Heteroscedastic Model.4.6 Empirical Example: CO2 Emission Data.4.7 Problems.5 Serial Correlation Model.5.1 Overview.5.2 Upper Bound for the Risk Matrix of a GLSE.5.3 Upper Bound Problem for a GLSE in the Anderson Model.5.4 Upper Bound Problem for a GLSE in a Two-equation Heteroscedastic Model.5.5 Empirical Example: Automobile Data.5.6 Problems.6 Normal Approximation.6.1 Overview.6.2 Uniform Bounds for Normal Approximations to the Probability Density Functions.6.3 Uniform Bounds for Normal Approximations to the Cumulative Distribution Functions.6.4 Problems.7 Extension of Gauss-Markov Theorem.7.1 Overview.7.2 An Equivalence Relation on S(n).7.3 A Maximal Extension of the Gauss-Markov Theorem.7.4 Nonlinear Versions of the Gauss-Markov Theorem.7.5 Problems.8 Some Further Extensions.8.1 Overview.8.2 Concentration Inequalities for the Gauss-Markov Estimator.8.3 Efficiency of GLSEs under Elliptical Symmetry.8.4 Degeneracy of the Distributions of GLSEs.8.5 Problems.9 Growth Curve Model and GLSEs.9.1 Overview.9.2 Condition for the Identical Equality between the GME and the OLSE.9.3 GLSEs and Nonlinear Version of the Gauss-Markov Theorem .9.4 Analysis Based on a Canonical Form.9.5 Efficiency of GLSEs.9.6 Problems.A. Appendix.A.1 Asymptotic Equivalence of the Estimators of theta in the AR(1) Error Model and Anderson Model.Bibliography.Index.
308 citations