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This book is concerned with data in which the observations are independent and in which the response is multivariate. Anthony Atkinson has been Professor of Statistics at the London School of Economics since 1989. Before that he was a Professor at Imperial College, London. He is the author of Plots, Transformations, and Regression, co-author of Optimum Experimental Designs, and joint editor of The Fascination of Statistics, a volume celebrating the centenary of the International Statistical Institute. Professor Atkinson has served as editor of The Journal of the Royal Statistical Society, Series B and as associate editor of Biometrika and Technometrics. He has published well over 100 articles in these and other journals including The Annals of Statistics, Biometrics, The Journal of the American Statistical Association, and Statistics and Computing. Marco Riani, after receiving his Ph.D. in Statistics in 1995 from the University of Florence, joined the Faculty of Economics at Parma University as postdoctoral fellow. In 1997 he won the prize for the best Italian Ph.D. thesis in Statistics. He is currently Associate Professor of Statistics in the University of Parma.He has published in Technometrics, The Journal of Computational and Graphical Statistics, The Journal of Business and Economic Statistics, The Journal of Forecasting, Environmetrics, Computational Statistics and Data Analysis, Metron, and other journals.
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This book is about using graphs to understand the relationship between a regression model and the data to which it is fitted. Because of the new way in which models are fitted, for example by least squares, we can lose information about the effect of individual observations on inferences about the form and parameters of the model. The methods developed in this book reveal how the fitted regression model depends on individual observations and on groups of observations. Robust procedures can sometimes reveal this structure, but downweight or discard some observations. The novelty in this book is to combine robustness and a "forward" search through the data with regression diagnostics and computer graphics.
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Why We Wrote This Book This book is about using graphs to explore and model continuous multi variate data. Such data are often modelled using the multivariate normal distribution and, indeed, there is a literatme of weighty statistical tomes presenting the mathematical theory of this activity. Our book is very dif ferent. Although we use the methods described in these books, we focus on ways of exploring whether the data do indeed have a normal distribution. We emphasize outlier detection, transformations to normality and the de tection of clusters and unsuspected influential subsets. We then quantify the effect of these departures from normality on procedures such as dis crimination and duster analysis. The normal distribution is central to our book because, subject to our exploration of departures, it provides useful models for many sets of data. However, the standard estimates of the parameters, especially the covari ance matrix of the observations, are highly sensitive to the presence of outliers. This is both a blessing and a curse. It is a blessing because, if we estimate the parameters with the outliers excluded, their effect is appre ciable and apparent if we then include them for estimation. It is however a curse because it can be hard to detect which observations are outliers. We use the forward search for this purpose.
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This book is about using graphs to understand the relationship between a regression model and the data to which it is fitted. The methods developed in this book reveal how the fitted regression model depends on individual observations and on groups of observations.
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Extensions of the robust multiple regression model include Bayesian, heteroskedastic, time series and compositional regression, together with the clustering of regression models.
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This volume contains revised versions of selected papers presented at the biennial meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society, which was held in Parma, June 6-8, 2005. Sergio Zani chaired the Scientific Programme Committee and Andrea Cerioli chaired the Local Organizing Committee. The scientific programme of the conference included 127 papers, 42 in spe cialized sessions, 68 in contributed paper sessions and 17 in poster sessions. Moreover, it was possible to recruit five notable and internationally renowned invited speakers (including the 2004-2005 President of the International Fed eration of Classification Societies) for plenary talks on their current research work. Among the specialized sessions, two were organized by Wolfgang Gaul with five talks by members of the GfKl (German Classification Society), and one by Jacqueline J. Meulman (Dutch/Flemish Classification Society). Thus, the conference provided a large number of scientists and experts from home and abroad with an attractive forum for discussion and mutual exchange of knowledge. The topics of all plenary and specialized sessions were chosen to fit, in the broadest possible sense, the mission of CLADAG, the aim of which is "to further methodological, computational and applied research within the fields of Classification, Data Analysis and Multivariate Statistics". A peer-review refereeing process led to the selection of 46 extended papers, which are contained in this book.