Journal of the Japanese Society of Computational Statistics

ASYMPTOTIC PROPERTIES OF ESTIMATES OF THE POWER-TRANSFORMATION MODEL TO BIVARIATE GROUPED DATA

Toshimitsu Hamasaki, Masashi Goto

2005 Volume 18 Issue 1 Pages 1-19
Published: 2005
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.18.1

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We investigate the asymptotic properties of maximum likelihood estimates of the power-transformation model to bivariate grouped data discussed by Hamasaki and Goto (1998a). The previous works deal with the most elementary situations of bivariate and simple regressions. We consider the three situations, i.e., (i) both variables given in grouped form, (ii) only one variable given in grouped form and (iii) the response involving both grouped and ungrouped data. We also provide one example to illustrate the application of the proposed method.

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MULTIPLE COMPARISON PROCEDURE OF DUNNETT'S TYPE FOR MULTIVARIATE NORMAL MEANS

Tomohiro Nakamura, Tsunehisa Imada

2005 Volume 18 Issue 1 Pages 21-32
Published: 2005
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.18.21

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In this study we consider the multiple comparison of Dunnett's type for several multivariate normal means (Dunnett, 1955). We derive a formula to determine a critical value satisfying a specified significance level for our multiple comparison procedure. Alternatively we determine approximate critical values. Here we use two simple methods for the approximation based on Bonferroni's inequality and the product inequality respectively. Then we consider the power of the test. Here we focus on the all-pairs power among various kinds of definitions for the power of the test of multiple comparison. Finally we give some numerical examples regarding the critical value and the power of the test.

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ESTIMATION FROM PSEUDO PARTIAL LIKELIHOOD IN A SEMIPARAMETRIC CURE MODEL

Tomoyuki Sugimoto, Toshimitsu Hamasaki, Masashi Goto

2005 Volume 18 Issue 1 Pages 33-46
Published: 2005
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.18.33

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We consider a cure model identical to one discussed by Kuk and Chen (1992), Sy and Taylor (2000) and Peng and Dear (2000). The feature of this model is that one uses the logistic regression model for the cure rate and Cox's proportional hazards model for the latent distribution. We propose a new semiparametric estimation method in this model using a criterion named the pseudo partial likelihood. Simulation studies show that the proposed method is appropriate for practical use, compared with semiparametric estimation via the EM algorithm. An application to data from a breast cancer with three treatment arms of adjuvant therapy is given to illustrate the aspect of the proposed method.

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ONE-SAMPLE EXPLORATORY PROCEDURES AFTER SEARCHING THE UNDERLYING DISTRIBUTION

Taka-aki Shiraishi

2005 Volume 18 Issue 1 Pages 47-60
Published: 2005
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.18.47

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As statistical estimation procedures for location, the sample mean, Hodges and Lehman's R-estimator, and Huber's M-estimator are introduced in a one-sample model. The asymptotic distributional theory for the three estimators and simulated mean squared errors give the features of the respective estimators depending on the underlying distribution. Based on the features, we propose an estimation procedure selecting one of the three estimators after searching a distribution near to the underlying distribution. It is shown that the mean squared error of the new estimator is more stable than the three estimators.
Next, as distribution-free test procedures, the conditional t-test, Wilcoxon's signed rank test, and the M-test are introduced. Asymptotic relative efficiency and simulated power of the respective tests are investigated. Based on their features, we propose a stable test procedure selecting one of the three tests after searching a distribution near to the underlying distribution.

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SENSITIVITY ANALYSIS IN FUNCTIONAL REGRESSION MODELS FOR SCALAR RESPONSES

Norihiro Harasawa, Kaoru Fueda, Yutaka Tanaka

2005 Volume 18 Issue 1 Pages 61-73
Published: 2005
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.18.61

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In this paper, we propose a method of sensitivity analysis in functional regression models for scalar responses. We define a Cook's D type distance in functional regression analysis (FRA) based on two kinds of influence functions: 1) Empirical Influence Function (EIF), 2) Sample Influence function (SIF). In ordinary regression analysis (ORA), the Cook's D distance can be expressed as a function of residual and leverage. We define diagnostic statistics which correspond to residual and leverage in ORA, and show our Cook's D type distances in FRA are functions of these diagnostic statistics. We give a numerical example to show the properties of two types of Cook's D type distance and these diagnostic statistics.

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List of authors and titles: The 19th

2005 Volume 18 Issue 1 Pages 75-81
Published: 2005
Released on J-STAGE: December 09, 2009

DOIhttps://doi.org/10.5183/jjscs1988.18.75

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