Multivariate Two-Sided Tests for Normal Mean Vectors Based on Approximations of Likelihood Ratio Test

Assuming that all components of a normal mean vector are simultaneously non negative or non positive, we consider a multivariate two-sided test for testing whether the normal mean vector is equal to zero or not. Since the likelihood ratio test is accompanied with theoretical and computational complications, we discuss two kinds of approximations of the likelihood ratio test. One is based on a conservative critical value determined by a certain inequality. The other is constructed by the approximation of the likelihood ratio test proposed by Tang et al. (1989). We compare the likelihood ratio test and two kinds of approximations through numerical examples regarding critical values and the power of the test.     

Multiple comparison procedures for finding non-maximum normal means

Abstract

In this study, we discuss multiple comparison procedures for finding normal means which are not maximum among several normal means. Specifically, we propose the single step procedure, the sequentially rejective step down procedure and the step up procedure. For the single step procedure we determine the critical value for a specified significance level. For the sequentially rejective step down procedure and the step up procedure we determine the critical value at each step of the test for a specified significance level. For three procedures we formulate the power of the test under a specified alternative hypothesis. We give some numerical examples regarding critical values and power of the test intended to compare three procedures.     

Step-Up Procedure for Multiple Comparison with a Control for Multivariate Normal Means

In this study, we consider the multiple comparison with a control for multivariate normal means. Specifically, we construct a step-up procedure by referring to Dunnett and Tamhane (1992 Dunnett , C. W. , Tamhane , A. C. ( 1992 ). A step-up multiple test procedure . Journal of the American Statistical Association 87 : 162 – 170 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). We derive recursive formulae for determining the critical values of the step-up procedure for a specified significance level. Then we formulate the power of the test. Finally, we compare the step-up procedure with the single-step procedure proposed by Nakamura and Imada (2005 Nakamura , T. , Imada , T. ( 2005 ). Multiple comparison procedure of Dunnett's type for multivariate normal means . Journal of the Japanese Society of Computational Statistics 18 : 21 – 32 .[Crossref] , [Google Scholar]) and the step-down procedure proposed by Imada and Douke (2007 Imada , T. , Douke , H. ( 2007 ). Step down procedure for comparing several treatments with a control based on multivariate normal response . Biometrical Journal 49 ( 1 ): 18 – 29 .[Crossref], [Web of Science ®] , [Google Scholar]) in terms of numerical examples regarding the power of the test.     

Multivariate Two-Sided Tests for Normal Mean Vectors with Unknown Covariance Matrix

A numerically stable method is developed which computes seemingly tight bounds at a small computational cost relative to the model size, when that model size is large, for the unreliability and bounds for the unreliability using, respectively, exact and bounding failure/repair continuous-time Markov chain models of fault-tolerant systems with exponential failure and repair time distributions, in which repair is deferred until some condition on the collection of failed components is satisfied, and, then, proceeds until reaching the state without failed components, with failure rates much smaller than repair rates and not too different output rates from states with deferred repair.     

Social Theory and Self-Organization: Toward a Sociology of Postmodernism

Abstract Significant changes which represent a linguistic and semantic turn in social theory occurred between in the mid 1970's and the early 1980's. This turn indicates the importance of the social and public dimensions of symbolic meaning that has been distorted functionally by orthodox modernization theory. Modern society is characterized as penetrating the idea of functional primacy into various areas of social life, but in the 1980's skepticism about modernity increased markedly and fluctuation of modernity was resulted. In this paper I discuss the problem of symbolic meaning and fluctuation of modernity from the viewpoint of self-organization paradigm which emphasizes ‘order from fluctuation’ and self-reference, and review the possibility of a postmodern sociology through claiming the necessity to ask how anti-control systems can be built.     

Multiple comparison for checking differences among normal variances

In this study, we discuss multiple comparisons for checking differences among normal variances. Specifically, we consider the multiple comparison with a control and the all-pairwise multiple comparison. For the multiple comparison with a control we determine the critical value for pairwise comparison satisfying a specified significance level exactly and formulate the power of the test under a specified alternative hypothesis. For the all-pairwise multiple comparison we determine two kinds of conservative critical values for pairwise comparison for a specified significance level and calculate the power of the test by Monte Carlo simulation. Finally, we give some numerical examples regarding critical values and power of the test.     

Procedure for determining sample size at each stage in group sequential test

The purpose of our study is to propose a. procedure for determining the sample size at each stage of the repeated group significance, tests intended to compare the efficacy of two treatments when a response variable is normal. It is necessary to devise a procedure for reducing the maximum sample size because a large number of sample size are often used in group sequential test. In order to reduce the sample size at each stage, we construct the repeated confidence boundaries which enable us to find which of the two treatments is the more effective at an early stage. Thus we use the recursive formulae of numerical integrations to determine the sample size at the intermediate stage. We compare our procedure with Pocock's in terms of maximum sample size and average sample size in the simulations.     

Industrialization and the Regime of Social Mobility in Postwar Japan

Abstract  This paper examines the hypothesis that the fluidity and openness of social stratification increase with industrialization, by applying a path analysis of status attainment and a log-linear analysis of social mobility to data from National Survey on Social Stratification and Mobility carried out five times at ten-year intervals since 1955 in Japan. The following two points are clarified through this analysis. First, the status attainment regime was constant from 1955 to 1995; when the effects of opportunity expansion due to economic growth are controlled, the data do not provide evidence that the openness of social stratification improved; and the industrialism thesis on openness is actually an illusion caused by the effects of economic growth. Second, the mobility regime was constant from 1955 to 1985, but the data from the 1995 survey do not fit the previous pattern and suggest a transformation may be under way. Based on the above findings, I will note that dissolution of the mobility regime must be considered when discussing the reality of future social stratification.     

Successive comparisons between ordered normal means using isotonic regression estimators

In this study we discuss multiple comparison procedures for checking differences among a sequence of normal means with ordered restriction. Lee and Spurrier (1995 Lee, R.E., Spurrier, J.D. (1995). Successive comparisons between ordered treatments. J. Stat. Plann. Inference 43:323–330.[Crossref], [Web of Science ®] , [Google Scholar]) proposed a multiple comparison procedure which tests the difference between two adjacent means using the difference of sample means. In this study we propose a multiple comparison procedure modifying Lee and Spurrier's (1995 Lee, R.E., Spurrier, J.D. (1995). Successive comparisons between ordered treatments. J. Stat. Plann. Inference 43:323–330.[Crossref], [Web of Science ®] , [Google Scholar]) procedure using isotonic regression estimators instead of sample means. We determine the critical value for pairwise comparisons for a specified significance level. Furthermore, we formulate the power of the test. Finally, we give some numerical examples regarding critical values and power of the test intended to compare our procedure with Lee and Spurrier's (1995 Lee, R.E., Spurrier, J.D. (1995). Successive comparisons between ordered treatments. J. Stat. Plann. Inference 43:323–330.[Crossref], [Web of Science ®] , [Google Scholar]) procedure.