Kernel naive Bayes discrimination for high‐dimensional pattern recognition

Kernel discriminant analysis translates the original classification problem into feature space and solves the problem with dimension and sample size interchanged. In high‐dimension low sample size (HDLSS) settings, this reduces the ‘dimension’ to that of the sample size. For HDLSS two‐class problems we modify Mika's kernel Fisher discriminant function which – in general – remains ill‐posed even in a kernel setting; see Mika et al. (1999). We propose a kernel naive Bayes discriminant function and its smoothed version, using first‐ and second‐degree polynomial kernels. For fixed sample size and increasing dimension, we present asymptotic expressions for the kernel discriminant functions, discriminant directions and for the error probability of our kernel discriminant functions. The theoretical calculations are complemented by simulations which show the convergence of the estimators to the population quantities as the dimension grows. We illustrate the performance of the new discriminant rules, which are easy to implement, on real HDLSS data. For such data, our results clearly demonstrate the superior performance of the new discriminant rules, and especially their smoothed versions, over Mika's kernel Fisher version, and typically also over the commonly used naive Bayes discriminant rule.     

A model of the Canadian global exchange rate: A test of the 1970s

This comment points out some methodological weaknesses in the Canadian global exchange rate model and the associated efficiency tests of Marwah and Bodkin. The model is found to be inadequate for policy analysis.     

Teaching Perspectives on Cross-Cultural Psychology and Japanese Society

This article discusses educational aspects of cross-cultural psychology in relationship to Japanese society. After exploring the present status of cross-cultural psychology in Japan, the paper delineates the factual, theoretical, and methodological implications of cross-cultural psychology for the teaching of psychology in Japanese universities. It is argued that an area approach incorporating comparative research on Japanese society can add context, detail, historical perspective, new methodology, and interdisciplinary richness to classes otherwise relying on traditional journal articles and textbooks of cross-cultural psychology. Such an approach is deemed useful for cross-cultural psychology classes taking place both inside and outside Japan. The article concludes with an annotated bibliography of research on Japanese society.     

High dimensional asymptotics for the naive Hotelling T2 statistic in pattern recognition

Abstract

This paper examines the high dimensional asymptotics of the naive Hotelling T² statistic. Naive Bayes has been utilized in high dimensional pattern recognition as a method to avoid singularities in the estimated covariance matrix. The naive Hotelling T² statistic, which is equivalent to the estimator of the naive canonical correlation, is a statistically important quantity in naive Bayes and its high dimensional behavior has been studied under several conditions. In this paper, asymptotic normality of the naive Hotelling T² statistic under a high dimension low sample size setting is developed using the central limit theorem of a martingale difference sequence.     

Perceived Freedom and its Sociological Effects: An Inquiry into the Relationship Between Liberalism and Inequality

Abstract:  Individual freedom has been regarded as one of the most important criteria for a desirable society and life. Recently, the theories of liberalism and distributive justice have received increasing attention as a theoretical basis for tackling problems pertaining to socioeconomic inequality and poverty. However, few quantitative analyses focus on the meaning of freedom in the context of socioeconomic inequality and political order in an existing liberal-democratic society. In this paper, I construct a self-rated measure of freedom—the overall perceived freedom scale—and examine (1) whether socioeconomic inequality is related to inequality of freedom, (2) whether freedom is related to subjective well-being, and (3) whether freedom affects people's political attitude toward inequalities. Analyses using data from a 2005 Japanese national survey ( N  = 1320) reveal the following results: (1) people with higher personal income (not household income), higher education, and better health tend to perceive greater freedom, (2) people with higher perceived freedom are more likely to be satisfied with their life, and (3) individuals with higher perceived freedom are more likely to oppose the government's egalitarian policy, and their opposition is based on the liberal principle of freedom and self-responsibility. On the basis of these findings, the double-edged possibility of individual freedom and liberalism as an "enhancer" and "moderator" of socioeconomic inequalities and political conflicts is suggested.     

Asymptotics for penalised splines in generalised additive models

This paper discusses asymptotic theory for penalised spline estimators in generalised additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the ridge-corrected penalised spline estimator. Furthermore, the asymptotics for the penalised quasi-likelihood fit in mixed models are also discussed.     

Asymptotic theory for local estimators based on Bregman divergence

This article is concerned with asymptotic theory for local estimators based on Bregman divergence. We consider a localized version of Bregman divergence induced by a kernel weight and minimize it to obtain the local estimator. We provide a rigorous proof for the asymptotic consistency of the local estimator in a situation where both the sample size and the bandwidth involved in the kernel weight increase. Asymptotic normality of the local estimator is also developed under the same asymptotic scenario. Monte Carlo simulations are also performed to confirm the theoretical results. The Canadian Journal of Statistics 47: 628–652; 2019 © 2019 Statistical Society of Canada     

A model of the Canadian global exchange rate: A test of the 1970s

A review of the literature indicates that no single exchange rate model has been able to track successfully the movements of the Canadian dollar for both the 1970–1976 period and the period thereafter. The purchasing power parity model, irrespective of whether based on relative wholesale prices, unit labor costs, GNP deflators, or export prices performs very poorly; the monetarist models collapse because of their strict adherence to the purchasing power parity and interest rate parity assumptions; the portfolio demand models require a significant adjustment for the post-1976 period. This paper presents a medium-term eclectic model of the global exchange rate of the Canadian dollar and examines a spectrum of broad issues that reflect on the efficiency of the foreign exchange market of Canada. These issues are basically related to the interest parity assumption, the role of speculation, and the test of rational expectations. The global exchange rate is defined as the value of the Canadian dollar measured in terms of a unit of basket of currencies comprising currencies of France, West Germany, Japan, the U.K., and the USA. The model belongs to the same genre of balance of payments structural models that explain the exchange rates by balancing demand and supply of foreign currencies. The model simultaneously explains both spot and forward rates, and it has been estimated and tested by using the quarterly data for 1971–1981.     

Cross-Cultural Psychology in Japan

This article portrays the situation of cross-cultural psychology in Japan, including historical background, institutional aspects, and research findings by Japanese investigators. Reflecting the internationalization of Japanese society, cultural influences on human behavior have recently drawn the attention of Japanese psychologists, and the number of researchers engaged in cross-cultural investigations is steadily increasing. A review of articles in current Japanese journals suggests that most cross-cultural studies belong to the areas of social, educational, and developmental psychology where they increasingly focus on specific themes and hypotheses. Although cross-cultural psychologists interact in each research area, cross-cultural findings have only rarely been discussed or integrated on the common plane of cross-cultural psychology. In part, this is true because no association of cross-cultural psychology exists in Japan. The authors emphasize the importance of a systematic approach to response styles which influence research findings and the fruitfulness of comparing Japanese findings to those obtained in other non-Western societies.