Journal of the Japan Statistical Society, Japanese Issue

LATENT CLASS ANALYSIS FOR EXPLAINING A HIERARCHICAL LEARNING STRUCTURE

Nobuoki Eshima

1990 Volume 20 Issue 1 Pages 1-12
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.1

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In the present paper, a latent structure analysis for studying the systematic learning process of acquiring several skills is developed. The learning structure considered in this paper means not only the linear hierarchical learning structure but also the branching hierarchical learning structure. The acquisition of each skill is assessed on the basis of the response to the related binary item (Success or Failure), Further, it is assumed that each subject responds to each item stochastically, that is, we admit both guessing errors and forgetting errors. With regards to the model, the hypothesized structure is incorporated into the model itself within the framework of the latent class model. An algorithm for maximum likelihood estimation of the latent parameters (MLE algorithm) is constructed according to the EM algorithm. A numerical example is also presented to demonstrate the estimation procedure.

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PARSIMONIOUS QUASI-UNIFORM ASSOCIATION MODELS APPLIED TO DANISH OCCUPATIONAL MOBILITY DATA

Sadao Tomizawa

1990 Volume 20 Issue 1 Pages 13-22
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.13

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For the well-known Danish occupational mobility data describing, say, the crossclassification of father's and son's occupational status categories, the quasi-uniform association (QU) model considered by Goodman (1979, 1981b) fits well. This paper introduces some parsimonious QU models in which the odds of row and/or column effect paprameters pertaining to adjacent categories are given by an exponential function. For the Danish data, the parsimonious QU models introduced in this paper are preferable to the original QU model, and new interpretations are made.

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SOME REMARKS ON PRINCIPAL COMPONENT ANALYSIS AS A SUBSTITUTE FOR FACTOR ANALYSIS IN MONOFACTOR CASES

Manabu Sato

1990 Volume 20 Issue 1 Pages 23-31
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.23

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Principal Component Analysis (PCA) and Factor Analysis (FA) resemble each other but have rather different aims. However, PCA is used very often for the same purpose as FA without careful consideration. The present paper is an attempt to answer the following questions: (1) Can a substitute use be justified? (2) What attention should be paid to interpreting loadings calculated with PCA? Some results and typical tendencies in monofactor cases for a population are presented. Further, these are examined for certain empirical data.

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SEQUENTIAL SHRINKAGE ESTIMATION FOR A COEFFICIENT MATRIX IN A MULTIVARIATE REGRESSION MODEL

T. Kubokawa, A. K. E. Saleh

1990 Volume 20 Issue 1 Pages 33-42
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.33

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This paper considers the sequential estimation of the coefficient matrix in the multi variate regression model, where the covariance matrix is assumed to be fully unknown or to be diagonal and unknown. Shrinkage estimators exactly dominating the usual sequential estimator are developed and their risks are asymptotically compared.

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ADMISSIBILITY OF THE LIKELIHOOD RATIO TEST FOR LINEAR CONSTRAINTS

Nobuo Nishida

1990 Volume 20 Issue 1 Pages 43-49
Published: 1990
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.43

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In this paper, the testing problem for Hμ=ξ₀ and Σ=Σ₀ is considered. A class of admissible tests is provided for this problem, and an asymptotic expansion of the null distribution of the test statistic is derived. The class considered includes the likelihood ratio test.

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ASYMPTOTIC EXPANSIONS FOR E_θ(t) AND E_θ(^-x_t) WHICH APPEAR IN THE REPEATED SIGNIFICANCE TESTS FOR THE NORMAL MEANS

Hajime Takahashi

1990 Volume 20 Issue 1 Pages 51-60
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.51

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This paper continues the project of Takahashi (1987) to obtain asymptotic expansions forE_θ(t) and E_θ(^-x_t) up to the terms involving a^-1 and a^-2, respectively, as a→∞, where t is the one-sided stopping time for testing the hypothesis that the normal mean is zero.
AMS 1980 subject classifications. Primary 60F05, 62L12; secondary 60K05.

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A NUMERICAL COMPARISON OF NORMAL AND LARGE DEVIATION APPROXIMATION FOR TAIL PROBABILITIES

J. C. Fu, C. M. Leu, C. Y. Peng

1990 Volume 20 Issue 1 Pages 61-67
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.61

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In this paper, several numerical examples are given to show that the large deviation approximation for the tail probability is much superior to the classical normal approximation. It also shows that, even in the case of small or moderate sample sizes (10≤n≤50), the large deviation approximation performs very well, while the normal approximation performs poorly.

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ON THE UNIFORM INTEGRABILITY AND ALMOST SURE CONVERGENCE OF WEIGHTED SUMS

Kai Fun Yu

1990 Volume 20 Issue 1 Pages 69-75
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.69

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Let X, X₁, … be independent and identically distributed random variables with zero and finite absolute p-th moment for some p greater than or equal to two. For each positive integer n, let a_n1, …, a_nn be constants. The boundedness of {(a²_n1+…+a²_nn)/n^2/p, n≥1} is established to be a necessary and sufficient condition for the uniform integrability of {|∑a_niX_i/n^1/p|^p, n≥1}. Conditions are also given for the central limit thorem and the convergence in probability of {∑a_niX_i/n^1/p, n≥1}. An improvement of Thrum's (1987) theorem on the almost sure convergence is obtained. As a result, the moment convergence and its limits are established.

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TWO-STAGE ESTIMATORS WITH BOUNDED RISK IN A GROWTH CURVE MODEL

Tatsuya Kubokawa

1990 Volume 20 Issue 1 Pages 77-87
Published: 1990
Released on J-STAGE: August 24, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.77

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For a coefficient matrix in the growth curve model, this paper gives a two-stage estimation procedure, such that its risk function relative to arbitrary quadratic loss is bounded above by a preassigned constant, and its asymptotic efficiency is discussed. Also, for powers of the generalized variance, a procedure with a bounded risk is developed, and some domination results are shown.

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Empirical Studies in Finance: A Survey

Kazuhiko Nishina

1990 Volume 20 Issue 1 Pages 89-107
Published: 1990
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.89

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Based on an introductory review of the finance theory, we investigated the contemporary stage of the empirical studies in finance. Though a large number of researches have been conducted in various areas, several subjects are left to be done, especially for Japanese financial markets.
To make a further progress in these fields, it is required to correctly understand the new developement of the theory of finance.

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Book Reviews

[in Japanese], [in Japanese], [in Japanese], [in Japanese], [in Japane ...

1990 Volume 20 Issue 1 Pages 109-115
Published: 1990
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.20.109

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