Testing linear hypotheses of mean vectors for high-dimension data with unequal covariance matrices

We propose a new test procedure for testing linear hypothesis on the mean vectors of normal populations with unequal covariance matrices when the dimensionality, p exceeds the sample size N  , i.e. p/N→c<∞$p/N\to c<\infty$. Our procedure is based on the Dempster trace criterion and is shown to be consistent in high dimensions.     

The Asymptotic Approximation of EPMC for Linear Discriminant Rules Using a Moore-Penrose Inverse Matrix in High Dimension

We consider the discriminant rule in a high-dimensional setting, i.e., when the number of feature variables p is comparable to or larger than the number of observations N. The discriminant rule must be modified in order to cope with singular sample covariance matrix in high-dimension. One way to do so is by considering the Moor-Penrose inverse matrix. Recently, Srivastava (2006 Srivastava , M. S. ( 2006 ). Minimum distance classification rules for high dimensional data . J. Multivariate Anal. 97 : 2057 – 2070 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed maximum likelihood ratio rule by using Moor-Penrose inverse matrix of sample covariance matrix. In this article, we consider the linear discriminant rule by using Moor-Penrose inverse matrix of sample covariance matrix (LDRMP). With the discriminant rule, the expected probability of misclassification (EPMC) is commonly used as measure of the classification accuracy. We investigate properties of EPMC for LDRMP in high-dimension as well as the one of the maximum likelihood rule given by Srivastava (2006 Srivastava , M. S. ( 2006 ). Minimum distance classification rules for high dimensional data . J. Multivariate Anal. 97 : 2057 – 2070 .[Crossref], [Web of Science ®] , [Google Scholar]). From our asymptotic results, we show that the classification accuracy of LDRMP depends on new distance. Additionally, our asymptotic result is verified by using the Monte Carlo simulation.     

Simultaneous Tests for Independence Among Components of Random Vector by Step-Down Multiple Comparison Procedure

In this article, we consider testing independence among components of random vector in multivariate normal population. For testing independence, we use the modified likelihood ratio test statistic which is improved an approximation to χ² distribution of the likelihood ratio test statistic. In order to perform simultaneous tests for independence among components of random vector, we use the step-down multiple comparison procedure based on the closed testing procedure proposed by Marcus et al. (1976 Marcus , R. , Peritz , E. , Gabriel , K. R. ( 1976 ). On closed testing procedures with special reference to ordered analysis of variance . Biometrika 63 : 655 – 660 .[Crossref], [Web of Science ®] , [Google Scholar]). Finally, we perform Monte Carlo simulations and present numerical results.     

A Monte Carlo comparison of Jarque–Bera type tests and Henze–Zirkler test of multivariate normality

In the paper, tests for multivariate normality (MVN) of Jarque-Bera type, based on skewness and kurtosis, have been considered. Tests proposed by Mardia and Srivastava, and the combined tests based on skewness and kurtosis defined by Jarque and Bera have been taken into account. In the Monte Carlo simulations, for each combination of p = 2, 3, 4, 5 number of traits and n = 10(5)50(10)100 sample sizes 10,000 runs have been done to calculate empirical Type I errors of tests under consideration, and empirical power against different alternative distributions. Simulation results have been compared to the Henze–Zirkler’s test. It should be stressed that no test yet proposed is uniformly better than all the others in every combination of conditions examined.     

Mantel-Haenszel estimators for irregular sparse K2×J tables

This paper deals with sparse K2×J(J>2)$K2\times J(J>2)$ tables. Projection-method Mantel–Haenszel (MH) estimators of the common odds ratios have been proposed for K2×J$K2\times J$ tables, which include Greenland's generalized MH estimator as a special case. The method projects log-transformed MH estimators for all K2×2$K2\times 2$ subtables, which were called naive MH estimators, onto a linear space spanned by log odds ratios. However, for sparse tables it is often the case that naive MH estimators are unable to be computed. In this paper we introduce alternative naive MH estimators using a graph that represents K2×J$K2\times J$ tables, and apply the projection to these alternative estimators. The idea leads to infinitely many reasonable estimators and we propose a method to choose the optimal one by solving a quadratic optimization problem induced by the graph, where some graph-theoretic arguments play important roles to simplify the optimization problem. An illustration is given using data from a case–control study. A simulation study is also conducted, which indicates that the MH estimator tends to have a smaller mean squared error than the MH estimator previously suggested and the conditional maximum likelihood estimator for sparse tables.     

Gentrification without Gentry in a Declining Global City?: Vertical Expansion of Tokyo and Its Urban Meaning1

This article explores the reasons for the vertical expansion of cities till the 2020s by analyzing the history of urban space production for about half a century, using Tokyo as an example. As a concept, gentrification partially explains the changes in Tokyo. However, summarizing the entire urban transformation as a gentrification trend can lead to some misunderstandings. Most of the development took the form of simply rebuilding skyscrapers in limited areas, rather than the displacement of an entire class in the whole district. Consequently, the sharp contrast between island‐like skyscrapers and the densely populated small houses surrounding them became the typical landscape of current semi‐gentrified Tokyo. Instead of gentrification, “gentrification without gentry” would be a better expression for describing most cases in Tokyo. Alliances for urban speculation are always embedded in multi‐scale conditions in a globalizing world along with the inherent historical and structural constitution of the city. Through dynamic but contingent processes, a structure was constructed to promote urban development in a way that might exceed the actual demands. In the case of Tokyo, the bubble economy era and its effects, a would‐be global city ideology, mega‐events such as the Olympic Games, and expected earthquakes had a distinct influence on other common factors.     

Validity of Domain Satisfaction Across Cohorts in the US

Domain satisfaction, a relatively under-researched topic in subjective well-being research, is designed to capture satisfaction in multiple aspects of life (e.g., family, health). In view of the life course perspective, perceptions toward such different domains of life are most likely influenced by the historical and social climate that individuals uniquely experience over their life span. However, little is known about whether domain satisfaction is a valid measure across cohorts, which reflect differing life experiences at each life stage. This study examines the psychometric properties (e.g., validity and reliability) of a domain satisfaction measure across seven theoretically meaningful cohorts (e.g., Baby Boomers) using a nationally representative sample of American adults from multiple waves of the General Social Survey (n = 15,302). Results from confirmatory factor analysis showed that the validity of the domain satisfaction measure was not consistent across cohorts; unlike when all samples (e.g., cohorts were not considered) were analyzed together. A series of follow-up analyses also revealed that temporally proximate cohorts that were born around the same time were more likely to be psychometrically comparable, while temporally distant cohorts were not. In summary, this study provides empirical evidence suggesting that the validity of domain satisfaction is sensitive to cohort effects, and researchers need careful consideration when comparing cohorts chronologically further apart.     

Characterization of probability models by an odds ratio in prospective and retrospective studies

It is shown that, when exposure variables are continuous, the odds ratios are functions of exposure differences if and only if Cox's binary logistic models hold in a prospective framework, and if and only if the underlying distribution belongs to a family of exponential type distributions in a retrospective framework.