In problems of statistical inference, it is customary to use normal distribution as the basis of statistical analysis. Many results related to univariate analysis can be extended to multivariate analysis using multidimensional normal distribution, and statisticians have tried to broaden the scope of the distributions and achieve reasonable inferential conclusions.Â Â Zellner (1976) introduced the idea of using Student’s t-distribution, which can accommodate the heavier tailed distributions in a reasonable way and producing robust inference procedures for applications. Most of the research with Student’s t-distribution, so far, is focused on the agreement of the results with that of the normal theory. For example, the MLE of the location parameter agrees with of the mean-vector of a normal distribution. Similarly, the likelihood ratio test under the Student’s t-distribution has same distribution as the normal distribution under the null hypothesis.Â Â This book consists of thirteen chapters. Chapter 1 summarizes the results of various models under normal theory with brief review of the literature. Chapter 2 contains the basic properties of various known distributions and opens discussion of multivariate t-distribution and elliptically contoured distributions with their basic properties. Chapter 3Â discusses the statistical analysis of a location model from estimation of the intercept and slope to test of hypothesis of the parameters. The authors also add the preliminary test and shrinkage type estimators of the three parameters, which include the estimation of the scale parameter of the model while Chapter 4 contains similar details of a simple regression model. Chapter 5Â is devoted to ANOVA models and discussing on preliminary test and shrinkage type estimators in elliptically contoured distributions, and Chapter 6 deals with the parallelism model in the same spirit.Â Multiple regression models areÂ discussed inÂ Chapter 7, and ridge regression is addressedÂ in Chapter 8.Â Statistical inference ofÂ multivariate models and simple multivariate linear models are discussed in Chapter 9 and 10. Bayesian analysisÂ is discussed in elliptically contoured models in Chapter 11, and the statistical analysis of linear prediction models is included in chapter 12. The book concludes with Chapter 13, which isÂ devoted to shrinkage estimation.Â Additional topical coverage includes: location models; simple regression models; ANOVA; paralllelism models; multiple regression models; ridge regression; multivariate models; simple multivariate linear models; Bayesian analysis; linear prediction models; and Stein estimation.
Welcome to ANALYZE, designed to provide computer assistance for analyzing linear programs and their solutions. Chapter 1 gives an overview of ANALYZE and how to install it. It also describes how to get started and how to obtain further documentation and help on-line. Chapter 2 reviews the forms of linear programming models and describes the syntax of a model. One of the routine, but important, functions of ANALYZE is to enable convenient access to rows and columns in the matrix by conditional delineation. Chapter 3 illustrates simple queries, like DISPLAY, LIST, and PICTURE. This chapter also introduces the SUBMAT command level to define any submatrix by an arbitrary sequence of additions, deletions and reversals. Syntactic explanations and a schema view are also illustrated. Chapter 4 goes through some elementary exercises to demonstrate computer- assisted analysis and introduce additional conventions of the ANALYZE language. Besides simple queries, it demonstrates the INTERPRT command, which automates the analysis process and gives English explanations of results. The last 2 exercises are diagnoses of elementary infeasible instances of a particular model. Chapter 5 progresses to some advanced uses of ANALYZE. The first is blocking to obtain macro views of the model and for finding embedded substructures, like a netform. The second is showing rates of substitution described by the basic equations. Then, the use of the REDUCE and BASIS commands are illustrated for a variety of applications, including solution analysis, infeasibility diagnosis, and redundancy detection.
These three volumes constitute the edited Proceedings of the NATO Advanced Study Institute on Statistical Distributions in Scientific Work held at the University of Calgary from July 29 to August 10, 1974. The general title of the volumes is "Statistical Distributions in Scientific Work". The individual volumes are: Volume 1 - Models and Structures; Volume 2 - Model Building and Model Selection; and Volume 3 - Characterizations and Applications. These correspond to the three advanced seminars of the Institute devoted to the respective subject areas. The planned activities of the Institute consisted of main lectures and expositions, seminar lectures and study group dis- cussions, tutorials and individual study. The activities included meetings of editorial committees to discuss editorial matters for these proceedings which consist of contributions that have gone through the usual refereeing process. A special session was organized to consider the potential of introducing a course on statistical distributions in scientific modeling in the curriculum of statistics and quantitative studies. This session is reported in Volume 2. The overall perspective for the Institute is provided by the Institute Director, Professor G. P. Pati1, in his inaugural address which appears in Volume 1. The Linnik Memorial Inaugural Lecture given by Professor C. R. Rao for the Characterizations Seminar is included in Volume 3.
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