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The areas covered included topics in the analysis of repeated measurements, cluster analysis, discriminant analysis, canonical cor relations, distribution theory and testing, bivariate densi ty estimation, factor analysis, principle component analysis, multidimensional scaling, multivariate linear models, nonparametric regression, etc.

Use and misuse of statistics seems to be the signum temporis of past decades. In Part One we present the consecutive stages of formalization of statistical problems, i.e., the description of the experiment, the presentation of the aim of the investigation, and of the constraints put upon the decision rules.

After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975).

Econometrics as an applied discipline attempts to use information in a most efficient manner, yet the information theory and entropy approach developed by Shannon and others has not played much of a role in applied econometrics.

Fundamentals of Convex Analysis offers an in-depth look at some of the fundamental themes covered within an area of mathematical analysis called convex analysis.

Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Normative decision theory is much more formalized than descriptive theory.

It addresses contemporary research topics of interest such as intelligent control, genetic algorithms, neural networks, optimization techniques, expert systems, fractals, and computer vision.

The areas covered included topics in the analysis of repeated measurements, cluster analysis, discriminant analysis, canonical cor relations, distribution theory and testing, bivariate densi ty estimation, factor analysis, principle component analysis, multidimensional scaling, multivariate linear models, nonparametric regression, etc.

Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common.

Multivariate Statistical Analysis

The death of Professor K. C. Sreedharan Pillai on June 5, 1985 was a heavy loss to many statisticians all around the world. This volume is dedicated to his memory in recog­ nition of his many contributions in multivariate statis­ tical analysis. It brings together eminent statisticians Working in multivariate analysis from around the world. The research and expository papers cover a cross-section of recent developments in the field. This volume is especially useful to researchers and to those who want to keep abreast of the latest directions in multivariate statistical analysis. I am grateful to the authors from so many different countries and research institutions who contributed to this volume. I wish to express my appreciation to all those who have reviewed the papers. The list of people include Professors T. C. Chang, So-Hsiang Chou, Dipak K. Dey, Peter Hall, Yu-Sheng Hsu, J. D. Knoke, W. J. Krzanowski, Edsel Pena, Bimal K. Sinha, Dennis L. Young, Drs. K. Krishnamoorthy, D. K. Nagar, and Messrs. Alphonse Amey, Chi-Chin Chao and Samuel Ofori-Nyarko. I wish to thank Professors Shanti S. Gupta and James 0. Berger for their keen interest and encouragement. Thanks are also due to Cynthia Patterson for her help and Reidel Publishing Com~any for their cooperation in bringing this volume out.

Normative decision theory addresses itself to the question of how people ought to make decisions in various types of situations, if they wish to be regarded (or to regard themselves) as 'rational'. Normative decision theory is much more formalized than descriptive theory.