Journal of the Japan Statistical Society, Japanese Issue

CONSTRUCTION OF M-ESTIMATORS BY ROBUSTIFYING ORTHOGONAL POLYNOMIALS ASSOCIATED WITH THE DENSITY FUNCION

Manabu Iwasaki

1991 Volume 21 Issue 2 Pages 155-171
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.155

JOURNAL FREE ACCESS

Show abstractHide abstract

An approach to construct M-estimators is discussed. It is known, in various cases, that influence functions of maximum likelihood estimators are given in terms of certain orthogonal polynomials. In such cases, since such polynomials tend to infinity as x→±∞, the estimators are by no means robust against occurrence of gross errors. The method adopted in this paper is based on robustification of the influence functions which are given as functions of orthogonal polynomials corresponding to the density function. The present method has an advantage that it can automatically provide Fisher-consistent M-estimators to various problems as long as suitable orthogonal polynomials are available.
Applications of the present method to various estimation problems are also shown. Robust estimation of location and scale parameters of normal distributions is discussed in some depth. Other applications include estimation in life-time distributions (Gamma and Weibull distributions), estimation of correlation coefficient in bivariate normal distributions, and centering and sphering in projection pursuit.

View full abstract

Download PDF (725K)
DECOMPOSITIONS OF POLYNOMIAL DIAGONALS-PARAMETER SYMMETRY MODELS FOR SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES

Sadao Tomizawa

1991 Volume 21 Issue 2 Pages 173-180
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.173

JOURNAL FREE ACCESS

Show abstractHide abstract

For square contingency tables with ordered categories, this paper introduces polynomial diagonal marginal symmetry (PDMS) models. Tomizawa's (1990b) polynomial diagonals-parameter symmetry (PDPS) models are decomposed into the PDMS model and Goodman's (1979) diagonals-parameter symmetry model. It is noted that the likelihood ratio statistic for testing the PDPS model is equal to the sum of those for testing the decomposed models.

View full abstract

Download PDF (320K)
FINITE SAMPLE AND LARGE SAMPLE PROPERTIES OF THE OLS AND GRLS ESTIMATORS FOR A STRUCTURAL RELATIONSHIP WITH REPLICATION

Yoshiko Isogawa

1991 Volume 21 Issue 2 Pages 181-188
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.181

JOURNAL FREE ACCESS

Show abstractHide abstract

In a bivariate linear structural relationship with replication, we obtain the finite sample and large sample properties of the ordinary least-squares estimator (OLSE) and the grouping least-squares estimator (GRLSE) of the slope. We compare the two estimators and the maximum likelihood estimator (MLE). The accuracy of the asymptotic distribution of the GRLSE is discussed by using numerical computation.

View full abstract

Download PDF (273K)
THE MSE OF A PRE-TEST ESTIMATOR OF THE LINEAR REGRESSION MODEL WITH AN INTERVAL CONSTRAINT ON COEFFICIENTS

Hikaru Hasegawa

1991 Volume 21 Issue 2 Pages 189-195
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.189

JOURNAL FREE ACCESS

Show abstractHide abstract

A pre-test estimator in the linear regression model with an interval constraint on coefficients is considered. An MSE of the pre-test estimator, by using the two stage test, is derived and finally, the MSE performance of the pre-test estimator and the INCLS estimator are compared.

View full abstract

Download PDF (235K)
SMALL SAMPLE PROPERTIES OF THE INTERVAL CONSTRAINED LEAST SQUARES ESTIMATOR WHEN ERROR TERMS HAVE A MULTIVARIATE t DISTRIBUTION

Kazuhiro Ohtani

1991 Volume 21 Issue 2 Pages 197-204
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.197

JOURNAL FREE ACCESS

Show abstractHide abstract

This paper examines small sample properties of the interval constrained least squares (INCLS) estimator and the inequality constrained least squares (ICLS) estimator when error terms have a multivariate t distribution. It is shown that as the error terms depart from the normal distribution, the biases of the constrained estimators become slightly large; but the gain of using the constrained estimators is increased if the constraint is true.

View full abstract

Download PDF (296K)
EQUIREPLICATE VARIANCE-BALANCED DESIGNS FROM GROUP DIVISIBLE DESIGNS

D. K. Ghosh, Jyoti Divecha, Sanpei Kageyama

1991 Volume 21 Issue 2 Pages 205-209
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.205

JOURNAL FREE ACCESS

Show abstractHide abstract

Equireplicatc variance-balanced designs with unequal block sizes are systematically searched using some group divisible designs when suitable balanced incomplete block designs, with a required number of treatments, are not available. New designs are also given.

View full abstract

Download PDF (235K)
SERIES OF MAIN EFFECT PLUS ONE OR TWO PLANS FOR 2^m FACTORIALS WHEN THREE-FACTOR AND HIGHER ORDER INTERACTIONS ARE NEGLIGIBLE

Teruhiro Shirakura, Shinsei Tazawa

1991 Volume 21 Issue 2 Pages 211-219
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.211

JOURNAL FREE ACCESS

Show abstractHide abstract

This paper constructs a series of main effect plus k (=1, 2) plans for 2^m factorials in the absence of three-factor and higher order interactions. These plans are derived from balanced arrays of strength 4. In particular, the nonisomorphic simple graphs with 4 vertices are useful in obtaining plans for k=2. It is shown that the plans obtained for each m≥4 when k=1 and for each m≥5 when k=2, are of the minimum values of treatments among plans derived from balanced arrays of strength 4.

View full abstract

Download PDF (341K)
Tne Effect of Household Composition on Consumption and Estimation of Equivalence Scales: A Survey

Terukazu Suruga

1991 Volume 21 Issue 2 Pages 221-236
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.221

JOURNAL FREE ACCESS

Show abstractHide abstract

Equivalence scales express the change in the cost of attaining a certain welfare level when the household composition varies. They are very useful in deflating the budget of different household types to a needs-corrected basis. Though there are several sources for estimating equivalence scales, we only review the methods based on the data of household's expenditure in this paper. These methods are classified into two groups. The first group includes the methods which incorporate the household composition into the estimation of demand equations. The second group includes straightforward procedures for calculation just like the Paashe index or the Laspeyres index in price indicies. We survey several methods in these two groups.

View full abstract

Download PDF (996K)
Book Reviews

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

1991 Volume 21 Issue 2 Pages 237-249
Published: 1991
Released on J-STAGE: January 22, 2009

DOIhttps://doi.org/10.11329/jjss1970.21.237

JOURNAL FREE ACCESS

Download PDF (859K)

Register with J-STAGE for free!