Journal of the Japan Statistical Society, Japanese Issue

ON MALLOWS' Cp IN THE MULTIVARIATE LINEAR REGRESSION MODEL UNDER THE UNIFORM MIXED LINEAR CONSTRAINTS

Hikaru Hasegawa

1986 Volume 16 Issue 1 Pages 1-6
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.1

JOURNAL FREE ACCESS

Show abstractHide abstract

In this paper, we expand the Mallows' Cp into the multivariate linear regression model along the framework of Berndt and Savin [2]. Also, by using the Cp, we derive the optimal critical value for the Wald test in the multivariate linear regression model under the uniform mixed linear constraints.

View full abstract

Download PDF (200K)
DISTRIBUTIONS OF SOME STATISTICS IN HETEROSCEDASTIC INFERENCE METHOD

POWER FUNCTIONS AND PERCENTAGE POINTS

Hiroto Hyakutake, Minoru Siotani, Chu-yu Li, Mustafid

1986 Volume 16 Issue 1 Pages 7-20
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.7

JOURNAL FREE ACCESS

Show abstractHide abstract

Statistics in testing hypotheses and simultaneous confidence interval estimation on mean vectors of normal populations in the heteroscedastic case are considered. The asymptotic formulae for percentage points of the statistics are presented, based on which numerical tables are given. This paper is a continuation of the previous paper [3].

View full abstract

Download PDF (555K)
ROBUSTNESS OF 3-ASSOCIATE PBIB DESIGNS OF TWO TYPES

Sanpei Kageyama

1986 Volume 16 Issue 1 Pages 21-24
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.21

JOURNAL FREE ACCESS

Show abstractHide abstract

Using a necessary and sufficient condition for the connectedness of a 3-associate PBIB design, the robustness of 3-associate PBIB designs based on two association schemes (i.e., cubic, extended triangular) is shown in a sense of Ghosh [2].

View full abstract

Download PDF (168K)
ML CLASSIFICATION DISTANCES AND RULES IN THE NORMAL POPULATIONS WHEN COVARIANCE MATRICES ARE UNEQUAL

Mitsuyo Kanazawa

1986 Volume 16 Issue 1 Pages 25-36
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.25

JOURNAL FREE ACCESS

Show abstractHide abstract

Three classification rules in the discriminant problem of k normal populations having different covariance matrices are proposed. Each rule is based on a classification distance which is deduced by the likelihood procedure and defined as a distance from analogical inference of the Mahalanobis' distance. Classification rule-Z and-W for the different covariance matrices are shown to correspond to those of common covariance matrix. Classification rule-B takes into account the effect of sample size variation. The limiting distributions of these distances and associated statistics are studied. To compare these classification rules numerical examples are shown and their usefulness is discussed.

View full abstract

Download PDF (461K)
SENSITIVITY ANALYSIS IN HAYASHI'S SECOND METHOD OF QUANTIFICATION

Yutaka Tanaka, Tomoyuki Tarumi

1986 Volume 16 Issue 1 Pages 37-52
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.37

JOURNAL FREE ACCESS

Show abstractHide abstract

A method of sensitivity analysis is proposed for detecting influential observations in Hayashi's second method of quantification (discriminant analysis of categorical variables). It evaluates the changes of eigenvalues and the scores of categories due to a small change of the weights for a single or multiple individuals. The mathematical tool is the perturbation theory of eigenvalue problems which was used also in the investigations concerning Hayashi's third and fourth methods of quantification (Tanaka [14, 15, 16], Tarumi and Tanaka [17]). The perturbation theory used in the present paper covers not only the case where the eigenvalues of interest are all simple but also the case where there are some multiple eigenvalues among them.

View full abstract

Download PDF (724K)
SELECTION OF BEST NORMAL MEAN IN COMPLETE FACTORIAL EXPERIMENTS WITH INTERACTION AND WITH COMMON UNKNOWN VARIANCE

Baldeo K. Taneja

1986 Volume 16 Issue 1 Pages 53-65
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.53

JOURNAL FREE ACCESS

Show abstractHide abstract

In this paper, two two-stage selection procedures (factorial procedure FP and interaction procedure IP) are studied for the goal of selecting largest normal mean in complete factorial experiments with interactions and with common unknown variance. It is proven that procedure FP performs better than the procedure IP in terms of expected total sample size when there are no interactions in the model (in which case both the procedures satisfy probability requirement); and that procedure FP fails to satisfy the probability requirement whereas procedure IP does satisfy it when there are non-zero interactions in the model. It is noted that a procedure is being developed which acts as does FP when interactions are insignificant and as does IP when interactions are significant.

View full abstract

Download PDF (459K)
DATA-COMPATIBLE MODEL SELECTION AND A MINIMAX FAMILY OF MODEL SELECTION AND ESTIMATION PROCEDURES FOR A MULTIVARIATE NORMAL MEAN

Yasushi Nagata

1986 Volume 16 Issue 1 Pages 67-73
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.67

JOURNAL FREE ACCESS

Show abstractHide abstract

The inference procedure for the mean vector of a p-dimensional normal distribution with known variance-covariance matrix is considered under a loss function which evaluates both the error of model selection and that of estimation. The concept of “data-compatible model selection” is introduced. It is shown that procedures with data-compatible model selection and estimation by maximum likelihood estimator (m. l. e.) form a minimax family and that procedures with data-incompatible model selection and estimation by m. l. e. are not minimax.

View full abstract

Download PDF (306K)
CONDITIONS ON CONSISTENCY OF ESTIMATORS IN COVARIANCE STRUCTURE MODEL

Yutaka Kano

1986 Volume 16 Issue 1 Pages 75-80
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.75

JOURNAL FREE ACCESS

Show abstractHide abstract

This paper presents a condition that estimators in a covariance structure model are consistent weakly (strongly), which is equivalent to Shapiro's condition. The condition is composed of three parts, each of which is simpler and is checked more easily. This result is applied to a proof of consistency of estimators in a factor analysis model. The population value of a factor analysis model is given which does not admit any consistent estimator. This fact suggests that the proofs of consistency by the previous authors are not complete.

View full abstract

Download PDF (300K)
Estimation of Housing Price Index and Demand Price Elasticity for Urban Housing in Japan

Yoko Moriizumi

1986 Volume 16 Issue 1 Pages 81-100
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.81

JOURNAL FREE ACCESS

Show abstractHide abstract

Despite the many studies concerning the price elasticity of housing demand, no consensus has been obtained. Disaggreements of the elasticity estimates were originated from the different method of specifying the housing price index and from different data bases. The multidimensional character of housing makes direct observation of price impossible.
In this study, four different methods of specifying the price index of housing service using the same data have been applied for the estimation on the price elasticities of housing demand both in Tokyo metropolitan area and in 10 large cities in Japan. It has been found that the price elasticities of housing demand are from -0.4 to -0.3 (Tokyo, 1975), about -0.5 (Tokyo, 1976) and about -0.2 (10 cities, 1975).

View full abstract

Download PDF (1152K)
The Development of the Official Statistics in Japan

Sadanori Nagayama

1986 Volume 16 Issue 1 Pages 101-109
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.101

JOURNAL FREE ACCESS

Show abstractHide abstract

During the last ten decades the statistical system in Japan has been developed with the government statistics. This period can be divided into three parts; from 1870 to 1900, from 1900 to 1945 and from 1946 to 1980's. The developments of offiicial statistics in each part are reviewed in the first half of this paper. We now are in the fourth part and face to two opposite subjectse in the statistical system. One is the increasing needs for statistical data in various fields, the other is that it is not easy to enlarge further government statistical surveys to meet those needs since the environment of the statistical surveys has been set a limit. To resolve the above contradictory problems we have to utilize the available data sources in every directions. Not only do we depend on government statistical surveys but also non-governmental statistics. The large amount of administrative records stored by central and local government are also promising resources from which useful statistical data can be made.

View full abstract

Download PDF (618K)
Book Review

[in Japanese]

1986 Volume 16 Issue 1 Pages 111-112
Published: 1986
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.16.111

JOURNAL FREE ACCESS

Download PDF (104K)

Register with J-STAGE for free!