日本統計学会誌

LITTER EFFECTS TO DOSE-RESPONSE CURVE ESTIMATION

Eiji Yamamoto, Takemi Yanagimoto

1988 年 18 巻 2 号 p. 97-106
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.97

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The biases of the MLEs of a dose-response curve in the beta-binomial logistic model are studied when the model with a common litter effect is falsely applied to a set of data sampled from populations with different litter effects. The properties concerning biases are proved theoretically and the amount of biases is evaluated through numerical calculations and simulations. These results extend those of a simulation study of Kupper et al.

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ASYMPTOTIC ANCILLARITY IN TIME SERIES ANALYSIS

Masanobu Taniguchi, Ruriko Taniguchi

1988 年 18 巻 2 号 p. 107-121
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.107

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In time series inference for a spectral parameter, asymptotic ancillary statistic is constructed in terms of the maximum likelihood estimator and the observed Fisher information. It is shown that this ancillary statistic is second-order locally ancillary. Then we give a sufficient condition that the modified ancillary statistic is second-order asymptotically ancillary. Also the second-order Edgeworth expansion of the conditional distribution of the maximum likelihood estimator given the ancillary statistic is evaluated. Using this Edgeworth expansion we can calculate confidence intervals with probability levels to O(1/n), where n is the sample size. Then we investigate how the ancillary statistic gives suggestions. Some numerical studies are made and they show that our second-order approximation for the distribution of the ancillary statistic is good.

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EXACT MOMENTS OF THE MULTIVARIATE F AND BETA DISTRIBUTIONS

Yoshihiko Konno

1988 年 18 巻 2 号 p. 123-130
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.123

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Based on integration by parts formula, for the multivariate F and Beta distributions, second order moments of the matrices and those of inverse are obtained.

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AN EXPANSION OF THE GENERALIZED RIDGE ESTIMATOR IN A LINEAR REGRESSION MODEL

Takakatsu Inoue

1988 年 18 巻 2 号 p. 131-140
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.131

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In a linear regression model, it was shown by Hoerl and Kennard (1970a) that the generalized Ridge estimator has “potentially” smaller Mean Squared Error (MSE) as an alternative to the Ordinary Least Squares (OLS) estimator.
In this paper, we apply this estimator in a problem predicting a future objective variable on a prediction area different from a sample area, and we extend the generalized Ridge estimator with respect to the axes (column vectors of an orthogonal transformation matrix) on which we shrink with a diagonal matrix. A goodness of estimator is evaluated in the expectation of Prediction Mean Squared Error with respect to the future sample point.

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SOME CONSTRUCTIONS OF TWO-AND THREE-ASSOCIATE PBIB DESIGNS

Shakti Banerjee, Sanpei Kageyama

1988 年 18 巻 2 号 p. 141-147
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.141

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A new method of construction of two- and three-associate partially balanced incomplete block designs is proposed through an association scheme of a group divisible design. New non-isomorphic solutions are found.

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NONPARAMETRIC T-METHOD IN TWO-WAY LAYOUTS

Shin-ichi Matsuda

1988 年 18 巻 2 号 p. 149-155
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.149

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In a randomized block design with one or no observation per cell, we consider a nonparametric generalization of Tukey's T-method of multiple comparisons. Our generalization is based on aligned signed ranks given for every pair of treatments, and is like Hochberg's [1] GT2. The method is compared with Sen's [5] in terms of Pitman efficiency under the situation that there are no missing values. It is suggested that our method is better than Sen's [5], when there are many missing values.

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A-OPTIMAL BALANCED FRACTIONAL 2_m FACTORIAL DESIGNS OF RESOLUTION V WITH TWO BLOCKS, 4≤m≤6

Masahide Kuwada

1988 年 18 巻 2 号 p. 157-167
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.157

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Consider a balanced fractional 2_m factorial design of resolution V with two blocks derived from a balanced array (B-array) of strength 4. Furthermore, it is constructed by two subarrays with N₁ and N₂ assemblies (or treatment combinations), which are B-arrays of strength 2 and correspond to two blocks. In this paper, we present A-optimal designs with N (=N₁+N₂) assemblies for the following two cases: One is the case where N₂=N₁ if N is even and N₂=N₁+1 if N is odd, and N_k≤v(m), where v(m) is the number of the main effects and the two-factor interactions in the model assumed, i.e., v(m)=m+(_m²). The other is the case where v(m)≤N≤2v(m) and 1≤N_k≤v(m).
AMS 1980 subject classifications: Primary 62K05, Secondary 62K15.

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A GENERALIZATION OF MOSES RANK TEST

Shingo Shirahata

1988 年 18 巻 2 号 p. 169-175
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.169

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Moses (1963) proposed a rank test to test for the equality of scale parameters when location parameters are possibly different in the two-sample problem. In this paper, we consider a generalization of Moses test for the two-sample problem and investigate their asymptotic properties. It is found that the proposed tests are useful in the practical applications.

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ON THE MAXIMUM-ENTROPY DISTRIBUTION ON [0, ∞) WITH GIVEN FIRST TWO MOMENTS

Zyukiti Ikeda, Toshio Nishida

1988 年 18 巻 2 号 p. 177-185
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.177

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We are concerned with the maximum-entropy distribution on [0, ∞) with given mean m₁ and second moment m₂. For the case where m₂≤2m₁², we describe an algorithm for calculating the maximum-entropy distribution. In this case, if m₂→ m₁², the maximum-entropy distribution approaches the unit distribution degenerated at m₁, and if m²=2m₁² then the maximum-entropy distribution is the exponential distribution. For the other case where m₂>2m₁², we will show that there exists no maximumentropy distribution.

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A CENERALIZATION OF THE PRINCIPAL COMPONENT ANALYSIS

Takayuki Saito, Kariya Takeaki, Otsu Tatsuo

1988 年 18 巻 2 号 p. 187-193
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.187

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A nonlinear generalization of the principal component analysis (PCA) is made under normality. It is shown that this generalized PCA problem leads to an eigenvalue problem for the Hadamard products of the correlation matrix. In the framework of the generalized PCA, the result is applied to the problem of finding square-integrable continuous transformations.

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A SELECTED AND ANNOTATED BIBLIOGRAPHY ON THE ROBUSTNESS STUDIES TO NON-NORMALITY IN VARIANCE COMPONENT MODELS

R. A. Singhal, C. B. Tiwari, Hardeo Sahai

1988 年 18 巻 2 号 p. 195-206
発行日: 1988年
公開日: 2009/01/22

DOIhttps://doi.org/10.11329/jjss1970.18.195

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