Journal of the Japan Statistical Society, Japanese Issue

FINITE SAMPLE ECONOMETRICS USING ERA'S

P. C. B. Phillips

1984 Volume 14 Issue 2 Pages 107-124
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.107

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The paper considers approximate distribution theory as a way to deliver practical improvements over asymptotic methods. Trials of the adequacy of asymptotic series based approximations are conducted and the results exhibit the need for further improvements. An alternative approach is suggested which utilizes a family of extended rational approximants (ERA's). ERA's build on the strength of primitive exact theory or asymptotic series; they allow us to blend information from diverse analytic, numerical and experimental sources. The ultimate objective of the approach is to incorporate directly into software constructive functional approximants relevant to statistical practice. An illustration is provided.

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JOINT ASYMPTOTIC NORMALITY OF NONPARAMETRIC RECURSIVE DENSITY ESTIMATORS AT A FINITE NUMBER OF DISTINCT POINTS

Eiichi Isogai

1984 Volume 14 Issue 2 Pages 125-135
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.125

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Let x₁, …, x_n be independent and identically distributed R^P-valued random vectors with a common unknown density ƒ. We consider a recursive estimator ƒ_n consisting of kernel functions based on X₁, …, X_n. Let x₁, …, x_q be any distinct points on R^P. Under certain conditions, the joint asymptotic normality of (nh_??_)^1/2(ƒ_n(x₁)-ƒ(x₁), …, ƒ_n(x_q)-ƒ(x_q)) is shown.

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PARTIAL GAUSS-NEWTON ALGORITHM FOR LEAST-SQUARES AND MAXIMUM LIKELIHOOD METHODS IN FACTOR ANALYSIS

Masashi Okamoto, Masamori Ihara

1984 Volume 14 Issue 2 Pages 137-144
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.137

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An algorithm for both least-squares and maximum likelihood methods in exploratory factor analysis is presented. It replaces the Newton-Raphson method used in Jöreskog's algorithm by the Gauss-Newton method recommended by Lee and Jennrich for confirmatory factor analysis. It is shown to work well in practice.

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ASYMPTOTICALLY CLOSER ESTIMATORS FOR THE NORMAL COVARIANCE MATRIX

Nariaki Sugiura

1984 Volume 14 Issue 2 Pages 145-155
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.145

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In this paper, some estimators of a normal covariance matrix are compared based on the concept of asymptotic probability of closeness (=APC). The estimators proposed by Sugiura and Fujimoto [15] are shown to be asymptotically uniformly closer than Haff's estimator [2]. Several other estimators including the MLE, James and Stein's minimax estimators are also compared by the APC criterion. The closest scalar multiples of sample covariance matrix are derived.

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ASYMPTOTIC PROPERTIES OF SEVERAL ESTIMATORS OF THE AUTOCORRELATION BASED ON LIMITER ESTIMATING FUNCTIONS FOR A STATIONARY GAUSSIAN PROCESS WITH ADDITIVE OUTLIERS

Michihiro Yoshida, Masao Kondo, Nobuo Inagaki

1984 Volume 14 Issue 2 Pages 157-168
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.157

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We deal with the estimation of the autocorrelation of a stationary Gaussian process with additive outliers. The biases of several estimators of the autocorrelation based on limiter estimating functions are compared. We show the estimator due to Sen [11] is the least biased, namely the most robust among them.

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ON CONNECTEDNESS-CONDITIONS OF PBIB DESIGNS

G. M. Saha, Sanpei Kageyama

1984 Volume 14 Issue 2 Pages 169-178
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.169

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Ogawa, Ikeda and Kageyama (1984) gave a necessary and sufficient condition for the connectedness of an m-associate PBIB design by using a regular representation of the association algebra. In this note, the same result is derived by a very elementary approach. The expression given here is easy to apply and is a little different from theirs. Furthermore, the connectedness of various 3-associate PBIB designs is examined along with their robustness.

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ON A UNIFORM TWO-ARMED BANDIT PROBLEM

Toshio Hamada

1984 Volume 14 Issue 2 Pages 179-187
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.179

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Suppose that there are two experiments e⁰ and e¹, and by performing e0 or e¹, a random sample X or Y is obtained from the uniform distribution on the interval [0, p] or [0, q], respectively. The true values of p and q are unknown, but there is the prior knowledge that p and q have Pareto distributions as prior distributions. When x is obtained, the reward is x. Experiments can be made sequentially for n times, and at each time one of two experiments may be selected and performed. The objective is to maximize the total expected reward. This problem is formulated by dynamic programming and analyzed. It is found that there exists the function which describes the optimal strategy. Some properties of this function are derived.

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A COEFFICIENT OF CONCORDANCE BASED ON THE CHART OF LINKED LINES

Kazumasa Wakimoto, Shingo Shirahata

1984 Volume 14 Issue 2 Pages 189-197
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.189

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Suppose the observations of size n are ranked according to their magnitudes. In this article, a rank statistic considering the coefficient of concordance among such a m-rankings is proposed. This rank statistic is derived from the chart which consists of linked lines corresponding to the ranks. Its asymptotic distribution is dervied and it is compared with the Kendall's statistic. Some merits of our rank statistic are illustrated on the standpoint of graphical representation.

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[title in Japanese]

1984 Volume 14 Issue 2 Pages 199-218
Published: 1984
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.14.199

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