Discussion is made upon numerical computation for the distributions of the smallest and the largest latent roots of Wishart random matrices by numerically evaluating the series in zonal polynomials of high degree. Graphs for bivariate to quadrivariate distributions of the smallest latent root and for trivariate ones of the latter are shown for several values of parameters.
{"title":"NUMERICAL COMPUTATION ON DISTRIBUTIONS OF THE LARGEST AND THE SMALLEST LATENT ROOTS OF THE WISHART MATRIX","authors":"Hiroki Hashiguchi, N. Niki","doi":"10.5183/JJSCS1988.19.45","DOIUrl":"https://doi.org/10.5183/JJSCS1988.19.45","url":null,"abstract":"Discussion is made upon numerical computation for the distributions of the smallest and the largest latent roots of Wishart random matrices by numerically evaluating the series in zonal polynomials of high degree. Graphs for bivariate to quadrivariate distributions of the smallest latent root and for trivariate ones of the latter are shown for several values of parameters.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130298214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article focuses on a new characteristic quantity, "similarity distance", which is defined for a pair of time series data and reflects similarity between them. This characteristic quantity is defined with the help of a smooth approximating function, which is obtained by "WISAM (Wavelet Interpolation Method with Simulated Annealing)" developed by Mori (1999) and Mori and Misawa (2001). Afterwards, as an illustrated example of the usage of similarity distance together with WISAM, the classifications and similarity of the annual GDP data for ten regions in Japan are investigated.
本文重点研究了一个新的特征量“相似距离”，它是对时间序列数据进行定义，用来反映它们之间的相似度。该特征量通过平滑逼近函数定义，该函数由Mori(1999)和Mori and Misawa(2001)开发的“WISAM(小波插值方法与模拟退火)”获得。随后，以日本10个地区年度GDP数据的分类和相似性为例，研究了相似距离与WISAM方法的结合。
{"title":"SIMILARITY ANALYSIS OF TIME SERIES DATA BY WISAM","authors":"Takakazu Mori, T. Misawa","doi":"10.5183/JJSCS1988.19.15","DOIUrl":"https://doi.org/10.5183/JJSCS1988.19.15","url":null,"abstract":"This article focuses on a new characteristic quantity, \"similarity distance\", which is defined for a pair of time series data and reflects similarity between them. This characteristic quantity is defined with the help of a smooth approximating function, which is obtained by \"WISAM (Wavelet Interpolation Method with Simulated Annealing)\" developed by Mori (1999) and Mori and Misawa (2001). Afterwards, as an illustrated example of the usage of similarity distance together with WISAM, the classifications and similarity of the annual GDP data for ten regions in Japan are investigated.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124931111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"ESTIMATION FROM PSEUDO PARTIAL LIKELIHOOD IN A SEMIPARAMETRIC CURE MODEL","authors":"Tomoyuki Sugimoto, T. Hamasaki, M. Goto","doi":"10.5183/JJSCS1988.18.33","DOIUrl":"https://doi.org/10.5183/JJSCS1988.18.33","url":null,"abstract":"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.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115740610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"ASYMPTOTIC PROPERTIES OF ESTIMATES OF THE POWER-TRANSFORMATION MODEL TO BIVARIATE GROUPED DATA","authors":"T. Hamasaki, M. Goto","doi":"10.5183/JJSCS1988.18.1","DOIUrl":"https://doi.org/10.5183/JJSCS1988.18.1","url":null,"abstract":"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.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"326 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127285881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"SENSITIVITY ANALYSIS IN FUNCTIONAL REGRESSION MODELS FOR SCALAR RESPONSES","authors":"N. Harasawa, K. Fueda, Y. Tanaka","doi":"10.5183/JJSCS1988.18.61","DOIUrl":"https://doi.org/10.5183/JJSCS1988.18.61","url":null,"abstract":"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.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129268909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ONE-SAMPLE EXPLORATORY PROCEDURES AFTER SEARCHING THE UNDERLYING DISTRIBUTION","authors":"T. Shiraishi","doi":"10.5183/JJSCS1988.18.47","DOIUrl":"https://doi.org/10.5183/JJSCS1988.18.47","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115141682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"MULTIPLE COMPARISON PROCEDURE OF DUNNETT'S TYPE FOR MULTIVARIATE NORMAL MEANS","authors":"Tomohiro Nakamura, T. Imada","doi":"10.5183/JJSCS1988.18.21","DOIUrl":"https://doi.org/10.5183/JJSCS1988.18.21","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128969243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"CORRECT CLASSIFICATION RATES IN MULTIPLE CORRESPONDENCE ANALYSIS","authors":"K. Adachi","doi":"10.5183/JJSCS1988.17.1","DOIUrl":"https://doi.org/10.5183/JJSCS1988.17.1","url":null,"abstract":"","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125079365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Cox regression model is often used to evaluate effects of covariates on failure time distributions for competing risks survival data. We consider a situation where failure times are observed but failure types cannot be observed for some individuals, assuming that the probability of missing the type of a failure is identical for all failure types. Hemmi (1995) has proposed a maximum pseudo-partial likelihood estimator (MPPLE) of regression coefficients in the Cox model in order to improve the maximum partial likelihood estimator (MPLE). The MPPLE has consistency, but its distribution, which is required for interval estimation, has not analytically been obtained so far. This paper applies bootstrap methods such as the percentile and BCa methods to construct confidence intervals for the regression coefficients based on the MPPLE, and evaluates them numerically in terms of coverage probability and interval length. Simulation studies show that the bootstrap methods enable us to construct appropriate confidence intervals, and that the bootstrap confidence intervals based on the MPPLE are shorter than the confidence intervals given by the normal approximation based on the MPLE.
{"title":"A NUMERICAL STUDY ON BOOTSTRAP CONFIDENCE INTERVALS OF REGRESSION COEFFICIENTS IN THE COX MODEL FOR COMPETING RISKS WITH MISSING FAILURE TYPES","authors":"I. Hemmi","doi":"10.5183/JJSCS1988.17.33","DOIUrl":"https://doi.org/10.5183/JJSCS1988.17.33","url":null,"abstract":"The Cox regression model is often used to evaluate effects of covariates on failure time distributions for competing risks survival data. We consider a situation where failure times are observed but failure types cannot be observed for some individuals, assuming that the probability of missing the type of a failure is identical for all failure types. Hemmi (1995) has proposed a maximum pseudo-partial likelihood estimator (MPPLE) of regression coefficients in the Cox model in order to improve the maximum partial likelihood estimator (MPLE). The MPPLE has consistency, but its distribution, which is required for interval estimation, has not analytically been obtained so far. This paper applies bootstrap methods such as the percentile and BCa methods to construct confidence intervals for the regression coefficients based on the MPPLE, and evaluates them numerically in terms of coverage probability and interval length. Simulation studies show that the bootstrap methods enable us to construct appropriate confidence intervals, and that the bootstrap confidence intervals based on the MPPLE are shorter than the confidence intervals given by the normal approximation based on the MPLE.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133150818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Simultaneous confidence intervals for pairwise multiple comparisons among mean vectors under elliptical populations are considered. The estimation of simultaneous confidence intervals is given by using the approximate upper percentiles of the T2max statistic based on Bonferroni's inequality. In order to obtain the upper percentiles of the Tmax statistic, an asymptotic expansion for Hotelling's T2-type statistic under elliptical distributions is derived by the perturbation method. The accuracy and conservativeness of the approximations are evaluated via a Monte Carlo simulation study.
{"title":"PAIRWISE MULTIPLE COMPARISONS OF MEAN VECTORS UNDER ELLIPTICAL POPULATIONS WITH UNEQUAL SAMPLE SIZES","authors":"Naoya Okamoto, T. Seo","doi":"10.5183/JJSCS1988.17.49","DOIUrl":"https://doi.org/10.5183/JJSCS1988.17.49","url":null,"abstract":"Simultaneous confidence intervals for pairwise multiple comparisons among mean vectors under elliptical populations are considered. The estimation of simultaneous confidence intervals is given by using the approximate upper percentiles of the T2max statistic based on Bonferroni's inequality. In order to obtain the upper percentiles of the Tmax statistic, an asymptotic expansion for Hotelling's T2-type statistic under elliptical distributions is derived by the perturbation method. The accuracy and conservativeness of the approximations are evaluated via a Monte Carlo simulation study.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130515483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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