Diversity is characteristic of the information age and also of statistics. To date, the social sciences have contributed greatly to the development of handling data under the rubric of measurement, while the statistical sciences have made phenomenal advances in theory and algorithms. Measurement and Multivariate Analysis promotes an effective interplay between those two realms of research-diversity with unity. The union and the intersection of those two areas of interest are reflected in the papers in this book, drawn from an international conference in Banff, Canada, with participants from 15 countries. In five major categories - scaling, structural analysis, statistical inference, algorithms, and data analysis - readers will find a rich variety of topics of current interest in the extended statistical community.

These three volumes comprise the proceedings of the US/Japan Conference, held in honour of Professor H. Akaike, on the Frontiers of Statistical Modeling: an Informational Approach'. The major theme of the conference was the implementation of statistical modeling through an informational approach to complex, real-world problems. Volume 1 contains papers which deal with the Theory and Methodology of Time Series Analysis. Volume 1 also contains the text of the Banquet talk by E. Parzen and the keynote lecture of H. Akaike. Volume 2 is devoted to the general topic of Multivariate Statistical Modeling, and Volume 3 contains the papers relating to Engineering and Scientific Applications. For all scientists whose work involves statistics.

These three volumes comprise the proceedings of the US/Japan Conference, held in honour of Professor H. Akaike, on the `Frontiers of Statistical Modeling: an Informational Approach'. The major theme of the conference was the implementation of statistical modeling through an informational approach to complex, real-world problems. Volume 1 contains papers which deal with the Theory and Methodology of Time Series Analysis. Volume 1 also contains the text of the Banquet talk by E. Parzen and the keynote lecture of H. Akaike. Volume 2 is devoted to the general topic of Multivariate Statistical Modeling, and Volume 3 contains the papers relating to Engineering and Scientific Applications. For all scientists whose work involves statistics.

Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-of merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models."

This volume contains the Proceedings of the Advanced Symposium on Multivariate Modeling and Data Analysis held at the 64th Annual Heeting of the Virginia Academy of Sciences (VAS)--American Statistical Association's Vir ginia Chapter at James Madison University in Harrisonburg. Virginia during Hay 15-16. 1986. This symposium was sponsored by financial support from the Center for Advanced Studies at the University of Virginia to promote new and modern information-theoretic statist ical modeling procedures and to blend these new techniques within the classical theory. Multivariate statistical analysis has come a long way and currently it is in an evolutionary stage in the era of high-speed computation and computer technology. The Advanced Symposium was the first to address the new innovative approaches in multi variate analysis to develop modern analytical and yet practical procedures to meet the needs of researchers and the societal need of statistics. vii viii PREFACE Papers presented at the Symposium by e1l11lJinent researchers in the field were geared not Just for specialists in statistics, but an attempt has been made to achieve a well balanced and uniform coverage of different areas in multi variate modeling and data analysis. 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."

Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-of merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models."

These three volumes comprise the proceedings of the US/Japan Conference, held in honour of Professor H. Akaike, on the Frontiers of Statistical Modeling: an Informational Approach'. The major theme of the conference was the implementation of statistical modeling through an informational approach to complex, real-world problems. Volume 1 contains papers which deal with the Theory and Methodology of Time Series Analysis. Volume 1 also contains the text of the Banquet talk by E. Parzen and the keynote lecture of H. Akaike. Volume 2 is devoted to the general topic of Multivariate Statistical Modeling, and Volume 3 contains the papers relating to Engineering and Scientific Applications. For all scientists whose work involves statistics.

These three volumes comprise the proceedings of the US/Japan Conference, held in honour of Professor H. Akaike, on the Frontiers of Statistical Modeling: an Informational Approach'. The major theme of the conference was the implementation of statistical modeling through an informational approach to complex, real-world problems. Volume 1 contains papers which deal with the Theory and Methodology of Time Series Analysis. Volume 1 also contains the text of the Banquet talk by E. Parzen and the keynote lecture of H. Akaike. Volume 2 is devoted to the general topic of Multivariate Statistical Modeling, and Volume 3 contains the papers relating to Engineering and Scientific Applications. For all scientists whose work involves statistics.

This volume contains the Proceedings of the Advanced Symposium on Multivariate Modeling and Data Analysis held at the 64th Annual Heeting of the Virginia Academy of Sciences (VAS)--American Statistical Association's Vir ginia Chapter at James Madison University in Harrisonburg. Virginia during Hay 15-16. 1986. This symposium was sponsored by financial support from the Center for Advanced Studies at the University of Virginia to promote new and modern information-theoretic statist ical modeling procedures and to blend these new techniques within the classical theory. Multivariate statistical analysis has come a long way and currently it is in an evolutionary stage in the era of high-speed computation and computer technology. The Advanced Symposium was the first to address the new innovative approaches in multi variate analysis to develop modern analytical and yet practical procedures to meet the needs of researchers and the societal need of statistics. vii viii PREFACE Papers presented at the Symposium by e1l11lJinent researchers in the field were geared not Just for specialists in statistics, but an attempt has been made to achieve a well balanced and uniform coverage of different areas in multi variate modeling and data analysis. 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."