Journal of the Japanese Society of Computational Statistics

BOOTSTRAPPING K-MEANS CLUSTERING

Myoungshic Jhun

1990 Volume 3 Issue 1 Pages 1-14
Published: 1990
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.3.1

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Independent observations X₁, X₂, …, X_n are made on a distribution F on R^d. To devide these observations into k clusters, first choose a vector of optimal cluster centers b_n=(b_n1, b_n2, …, b_nk) to minimize W_n(a)=1/nΣni=1min₁≤j≤k||X_i-a_j||² as a function of a=(a₁, a₂, …, a_k), then assign each observation to its nearest cluster center. Each b_nj is the mean of observations in its cluster. Pollard (1982) obtained a central limit theorem for the means of the k-clusters. In this paper, it is shown that the bootstrap distribution of the centered b_n has the same limiting distribution; the argument rests on asymptotic behavior of empirical processes on Vapnik-Chervonenkis classes in triangular array setting. Advantages of the bootstrap methods are discussed and the performance of bootstrap confidence sets is compared with Pollard's confidence sets by Monte Carlo simulation. ²

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KNOWLEDGE-BASED VARIABLE SELECTION FOR TWO STAGE LEAST SQUARES USING PRINCIPAL COMPONENTS

Haruo Onishi

1990 Volume 3 Issue 1 Pages 15-24
Published: 1990
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.3.15

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Both economic and econometric knowledge are needed to estimate and adopt an equation. Economic knowledge is represented by the meanings of possible explanatory variables for an explained variable, the magnitudes concerning their coefficients, the functional form of the equation, and the constraints and hypotheses concerning their coefficients. Econometric knowledge for 2SLS using principal components is the classificationss of variables, t-test, Durbin-Watson test, Basmann test, standardized residual test, turning point test, and fitting test. It is important to make a computer process knowledge of applied econometricians. The Researcher System OEPP which can process them may reduce drastically research time and cost and improve applied econometrics.

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THE M-P INVERSE FOR THE BALANCED FACTORIAL DESIGN WITH INTERACTIONS

Byung Chun Kim, Ha Sik Sunwoo

1990 Volume 3 Issue 1 Pages 25-33
Published: 1990
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.3.25

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The M-P inverse of the design matrix for a balanced factorial design with interactions can be computed by an iterative procedure using the M-P inverse of a partitioned matrix. From this result we can easily obtain the projection matrix P_X=XX⁺ of the model y=Xβ+ε. Also matrices that result at each iteration are useful to compute sums of squares in analysis of variance. To obtain the projection matrix and sums of squares it is not necessary to compute any inversion of matrices but they can be obtained by multiplications of matrices.

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ON SOME ROLES OF KNOWLEDGE FUNCTIONS IN STATISTICAL SOFTWARE

Koji KURIHARA

1990 Volume 3 Issue 1 Pages 35-44
Published: 1990
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.3.35

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One of the most important roles to be filled in statistical software is to serve a user with useful statistical knowledge as a teaching or system lead software. In this paper, some properties of methodologies are numerically evaluated by algorithms based on Monte Carlo technique for the assistance of statistical data analysis in such statistical knowledge. These techniques are prepared to investigate or to learn the methodologies under a variety of conditions and assumptions. These functions are realized in statistical software NISAN by authors, and the properties of methodologies, power functions, relative efficiency, overall significance level of a test process and stability and reliability of analyzed output are given to illustrate the numerical evaluation under complicated situations.

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TEMPORAL SUMMARY TABLE MANAGEMENT SYSTEM AND ITS GRAPHIC INTERFACE

Jinho Kim, Yoonjoon Lee, Byungchun Kim

1990 Volume 3 Issue 1 Pages 45-59
Published: 1990
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.3.45

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There are many application s of databases, such as CAD/CAM, Office Automation, and Scientific/Statistical applications, that require not only current data but also past data. For such kind of applications, temporal databases maintain all evolution history of data. The history of data will be frequently used to analyze past and current data and to forecast the future. In this paper, we implement a system supporting statistical analysis of temporal databases. The system provides summary tables on temporal databases which are tabular representation of summary statistics obtained from source databases. The system also provides a graphic user interface displaying the data of summary tables in graphical forms such as histograms, graphs, and diagrams. These forms are useful for statistical analysis thus can help users to make a decision

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AN EXPERT SYSTEM FOR DATA ANALYSIS S/EXP AND ITS EFFECTIVENESS

Yuichi Ishibashi, Keiko Takeda

1990 Volume 3 Issue 1 Pages 61-67
Published: 1990
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.3.61

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Many kinds of statistical software are available, but most of them require the knowledge and experience of statistics. In such a circumstance a beginner of data analysis usually meets troubles when he starts an analysis without any advisors. We have developed an expert system for data analysis, we call it S/EXP. It is an expert system using S^***. The system incorporates knowledge and experience of statistics. At present it contains only regression analysis among various possible procedures and the incorporated knowledge and experience are limited, but its effectiveness is recognized. We discuss the possibilities and problems of expert systems for data analysis.

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