This paper consists of four independent surveys on various aspects of the theory of statistical inference. The first chapter by T. Kubokawa surveys recent developments in decision theoretic estimation theory focusing on shrinkage type estimation procedures. The second chapter by S. Eguchi treats statistical asymptotic theory from differential geometrical viewpoint. The third chapter by A. Takemura surveys various topics of testing hypotheses. The final chapter by S. Konishi surveys recent developments in Bootstrap methodology.

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Multivariate analysis is generically known as a collection of statistical notion, methods and theory on multivariate data of several variables. In general, there are two directions in the course of research in multivariate analysis. One lays stress on the research of statistical inference, assuming probability distributions for multivariate data. The other is free from the assumptions of probability distributions, and lays stress on reduced representations, etc. of multivariate data. In the latter case, various methods have been proposed for qualitative or multi-way data as well as conventional multivariate data. The former is called multivariate statistical analysis, and the latter is called multivariate data analysis. Strictly speaking, these two directions cannot be discriminated. On the other side, it is natural that one should create a system of multivariate statistical methods, making up for the two directions each other. However, at the present time great progress is being made in two directions, and two directions are rather independently developing. From these reasons we first divide multivariate statistical methods into methods related to statistical inference and those related to multivariate data analysis, and discuss current perspectives and future developments in some topics of methods. The contributor of Part I: Multivariate Statistical Inference is Yasunori Fujikoshi, and the contributor of Part II: Multivariate Data Analysis is Haruo Yanai. In the last part of Part III we list books and proceedings on multivariate analysis, discriminating these into various areas. The contents of this paper are as follows:

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In this survey article, a general view of the methodology of latent structure analysis is presented and some directions of further development are introduced. In the first section, the background of the latent structure analyses is described with the aim of the present article. In the subsequent sections, 2, 3 and 4, latent trait models, latent class models and latent structural equation model are discussed.

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Recent developments and perspectives of statistical time series analysis are shown by taking the focus on some topics. The paper is formed of two main parts. The first part is related to general theories of statistical time series analysis and the second one is related to specific topics in some special fields. In the first part, we discuss statistical inferences by parametric and non-parametric methods, prediction and so on. In the second part, we deal with specific topics in the fields of Economics, Engineering and Marine Technology.

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Statistical methods in Earth Sciences using useful models of time series, point processes and space-time processes are developping in conjunction with a variety of concrete applications. In the present paper, such models and methods successfully applied in seismology and related science of solid earth are reviewed. Particular emphasis is place don point process models in application to the analysis of seismic activity. Also, some developping models for analyzing various aspect of seismic wave data are intensively reviewed in section 9. Further, a number of remakable contributions of Japanese statisticians to some areas in earth sciences are also introduced in section 10.

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This paper surveys statistical issues appeared in pre-clinical experiments. From methodological point of view, strategies for multiplicities, estimation of effective dose, analysis of sequential data, and utilization of historical controls are discussed. From toxicological point of view, problems related to carcinogenicity, mutagenicity, teratogenicity, and behavioral toxicity are discussed. The author anticipates that muchprogress will be achieved if the importance of close collaboration between toxicologists and statisticians are realized.

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While the general principles of data analysis apply also to clinical trials, such trials have yet special features. First there are many sorts of variation factors such as institutes, severity of illness and cause germs, which are fixed and indicative factor within a trial but act as if they were noise in the actual clinical treatments. We describe for the model based approach to this problem the generalized linear models including the proportional hazards model, logistic regression and regression models for ordinal categorical data. It requires, however, a careful examination of the model before extending the result beyond the trial and in some cases the double-blind randomized design based approach is recommended, which is described in § 2. Next in the analysis of clinical trials mostly concerned are the nonnormal distributions and the method based on the rank data can be applied for the ordinal categorical data, and vice versa. The analysis of repeated measures is a developing field of which we introduce generalized multivariate analysis of variance approach, two-stage mixed effects model and nonlinear mixed effects model. Other important issues discussed are various kinds of multiplicity problems and proving equivalence of a new drug with the standard.

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This paper reviews biostatstical methods in epidemiologic studies for causal inference between a risk factor and a disease. After a brief introduction into measures of exposure effect which are of interest in epidemiologic research, classical epidemiologic designs, i.e. cohort and case-control studies, for effect estimation are illustrated. Recent developments in biostatistics and epidemiology allow to propose new study designs, such as nested case-control, case-cohort, and two-stage case-control studies. Some aspects of causal inference in epidemionlogic observational studies are discussed. Other important topics, misclassification errors, ecological bias, and longitudinal studies, are briefly reviewed.

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This paper is a survey of the econometric studies on macro and sectoral behavior in Japan over the last 10 to 15years. The survey is divided into two parts. After reviewing the main characteristics of recent econometric modeling efforts, the first part concerns with macro or economy-wide econometric model buildings. Here, major econometric models of Japan including a global international model are compared in terms of structural specification and fiscal policy multiplier.
The second part reports the results of empirical studies on sectoral behavior, namely those on business fixed investment demand and production-cost function in the business firm, and those on consumption-saving behavior in the household sector. As for the business fixed investment demand function, the empirical results based on Tobin's q theory are surveyed and are critically examined in terms of theoretical specification and statistical validity. Econometric studies on production and cost functions are assessed focusing on factor substitutability, technical progress, scale economy and economy of scope. Turning to the household behavior, a brief survey is made on the recent development in the consumption-saving analysis along Life Cycle-Permanent Income Hypothesis initiated by R. Hall. Then, the discussions concerning Japan's high saving rate are empirically examined, followed by empirical analysis of consumption expenditure pattern, asset portfolio and labor supply behavior.

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In this paper, some diagnostic tests in econometrics are surveyed from the pedagogical point of view. The diagnostic test is the general naming for testing procedures against presumptions on regression equations. In particular, it includes presumptions associated with the error term and presumptions associated with the specification of the regression equations. Tests for the serial correlation are explained in the first chapter, followed by tests heteroscedasticity, and normality. The ARCH model of heteroscedasticity and the RESET test for the specafication of the regression equation are also explained. The analysis on the non-stationary time series may be the most recent development in econometrics, and standard techniques of the unit-root tests, error correction model, and the cointegrations are reviewed in the last chapter.

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The purpose of this paper is to report the recent experiences in atatistical analysis with super-computer. In the case of nonlinear stochastic problem, computer-intensive approach is very useful for the method of simulated moments, where numerical solution of nonlinear function is calculeted effectively, or bootstrapping method are available. Super-computer is also powerful to present the property of complex structure of stochastic model graphically.

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This paper surveys the recent studies on income distribution in Japan with particular attention to empirical works. The present decade has experienced various revisions on tax system which involves the redistributive effect of income throughout the world. This stimulates the study for income distribution from various aspects. Some are made to clarify the present status of income distribution or others to evaluate the revisions. This survey reviews these new empirical results and shows that the income inequality for Japan ranks in the average among economically advanced western countries, which renews a widely believed knowledge that the income inequality in Japan is quite low.

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1. In this chapter, focusing the points on those issues as statistical organization and legislation on which the government statistical undertaking is based, the survey restricts itself only to the academic achievements. As far as the institutional system of official statistics is discussed from a standpoint of its fundamental role for statistics based on questionnaires, it crosses each other with theory of statistical survey. On the contrary an issue is raised on the need of expanded theory of statistical system which covers statistics based upon administrative records or registers in addition to those based on questionnaires. As a result of the survey, a few subjects of future researches are suggested.
2. In this chapter, we examined the problems about government statistical surveys caused by the changes in the modes of life and economic activities of thier respondents. Then the new developments of statistical techniques and statistical classification practices brought about by the diversification and the globalization of economic activities of Japanese enterprises in recent years are reviewed. Lastly the growing difficulties of the fieldwork of statistical surveys such as non-responses and non-cooperation of their respondents reflecting in the various surveys are summarized.
3. Treatise on data has been extensively discussed with the problems on the statistical survey system. This chapter reviews new developments in dataology and refers to the statistical database construction.

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