Anthony C. Atkinson

Measurement, regression, and calibration

3. Measurement, Regression, and Calibration. By P. J. Brown. ISBN 0 19 852245 2. Oxford University Press, Oxford, 1993. 212 pp. £27.50.

Plots, transformations, and regression : an introduction to graphical methods of diagnostic regression analysis

Thank you very much for reading plots transformations and regression an introduction to graphical methods of diagnostic regression analysis. Maybe you have knowledge that, people have look numerous times for their favorite readings like this plots transformations and regression an introduction to graphical methods of diagnostic regression analysis, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they are facing with some infectious bugs inside their laptop.This handbook provides a detailed, down-to-earth introduction to regression diagnostic analysis, a technique of growing importance for work in applied statistics. Heavily illustrated, with numerous examples to illuminate the discussion, this timely volume outlines methods for regression models, stressing detection of outliers and inadequate models; describes the transformation of variables in an equation, particularly the response; and considers such advanced topics as generalized linear models. A useful guide that combines lucid explanations with up-to-date research findings.

Fast Very Robust Methods for the Detection of Multiple Outliers

Abstract A few repeats of a simple forward search from a random starting point are shown to provide sufficiently robust parameter estimates to reveal masked multiple outliers. The stability of the patterns obtained is exhibited by the stalactite plot. The robust estimators used are least median of squares for regression and the minimum volume ellipsoid for multivariate outliers. The forward search also has potential as an algorithm for calculation of these parameter estimates. For large problems, parallel computing provides appreciable reduction in computational time.

Exploring multivariate data with the forward search

Contents Preface Notation 1 Examples of Multivariate Data 1.1 In.uence, Outliers and Distances 1.2 A Sketch of the Forward Search 1.3 Multivariate Normality and our Examples 1.4 Swiss Heads 1.5 National Track Records forWomen 1.6 Municipalities in Emilia-Romagna 1.7 Swiss Bank Notes 1.8 Plan of the Book 2 Multivariate Data and the Forward Search 2.1 The Univariate Normal Distribution 2.1.1 Estimation 2.1.2 Distribution of Estimators 2.2 Estimation and the Multivariate Normal Distribution 2.2.1 The Multivariate Normal Distribution 2.2.2 The Wishart Distribution 2.2.3 Estimation of O 2.3 Hypothesis Testing 2.3.1 Hypotheses About the Mean 2.3.2 Hypotheses About the Variance 2.4 The Mahalanobis Distance 2.5 Some Deletion Results 2.5.1 The Deletion Mahalanobis Distance 2.5.2 The (Bartlett)-Sherman-Morrison-Woodbury Formula 2.5.3 Deletion Relationships Among Distances 2.6 Distribution of the Squared Mahalanobis Distance 2.7 Determinants of Dispersion Matrices and the Squared Mahalanobis Distance 2.8 Regression 2.9 Added Variables in Regression 2.10 TheMean Shift OutlierModel 2.11 Seemingly Unrelated Regression 2.12 The Forward Search 2.13 Starting the Search 2.13.1 The Babyfood Data 2.13.2 Robust Bivariate Boxplots from Peeling 2.13.3 Bivariate Boxplots from Ellipses 2.13.4 The Initial Subset 2.14 Monitoring the Search 2.15 The Forward Search for Regression Data 2.15.1 Univariate Regression 2.15.2 Multivariate Regression 2.16 Further Reading 2.17 Exercises 2.18 Solutions 3 Data from One Multivariate Distribution 3.1 Swiss Heads 3.2 National Track Records for Women 3.3 Municipalities in Emilia-Romagna 3.4 Swiss Bank Notes 3.5 What Have We Seen? 3.6 Exercises 3.7 Solutions 4 Multivariate Transformations to Normality 4.1 Background 4.2 An Introductory Example: the Babyfood Data 4.3 Power Transformations to Approximate Normality 4.3.1 Transformation of the Response in Regression 4.3.2 Multivariate Transformations to Normality 4.4 Score Tests for Transformations 4.5 Graphics for Transformations 4.6 Finding a Multivariate Transformation with the Forward Search 4.7 Babyfood Data 4.8 Swiss Heads 4.9 Horse Mussels 4.10 Municipalities in Emilia-Romagna 4.10.1 Demographic Variables 4.10.2 Wealth Variables 4.10.3 Work Variables 4.10.4 A Combined Analysis 4.11 National Track Records for Women 4.12 Dyestuff Data 4.13 Babyfood Data and Variable Selection 4.14 Suggestions for Further Reading 4.15 Exercises 4.16 Solutions 5 Principal Components Analysis 5.1 Background 5.2 Principal Components and Eigenvectors 5.2.1 Linear Transformations and Principal Components . 5.2.2 Lack of Scale Invariance and Standardized Variables 5.2.3 The Number of Components 5.3 Monitoring the Forward Search 5.3.1 Principal Components and Variances 5.3.2 Principal Component Scores 5.3.3 Correlations Between Variables and Principal Components 5.3.4 Elements of the Eigenvectors 5.4 The Biplot and the Singular Value Decomposition 5.5 Swiss Heads 5.6 Milk Data 5.7 Quality of Life 5.8 Swiss Bank Notes 5.8.1 Forgeries and Genuine Notes 5.8.2 Forgeries Alone 5.9 Municipalities in Emilia-Romagna 5.10 Further reading 5.11 Exercises 5.12 Solutions 6 Discriminant Analysis 6.1 Background 6.2 An Outline of Discriminant Analysis 6.2.1 Bayesian Discrimination 6.2.2 Quadratic Discriminant Analysis 6.2.3 Linear Discriminant Analysis 6.2.4 Estimation of Means and Variances 6.2.5 Canonical Variates 6.2.6 Assessment of Discriminant Rules 6.3 The Forward Search 6.3.1 Step 1: Choice of the Initial Subset 6.3.2 Step 2: Adding

Optimum Experimental Designs for Properties of a Compartmental Model

Three properties of interest in bioavailability studies using compartmental models are the area under the concentration curve, the maximum concentration, and the time to maximum concentration. Methods are described for finding designs that minimize the variance of the estimates of these quantities in such a model. These methods use prior information. Both prior estimates and prior distributions are used. The designs for an open one-compartment model are compared with the corresponding D theta-optimum design for all parameters and also with designs that minimize the sum of the scaled variances of the individual properties.

Optimum biased‐coin designs for sequential treatment allocation with covariate information

Randomized optimum designs of biased-coin type are compared with other strategies for the sequential allocation of two or more treatments in a clinical trial. The emphasis is on the variance of estimated treatment contrasts. This variance, which depends on the design strategy employed, may be interpreted as the number of patients on whom information is lost. Simulations provide clear plots of the evolution of this loss during the course of the clinical trial.

A Celebration of statistics : the ISI centenary volume

1. A Celebration of Statistics: The ISI Centenary Volume. Edited by A. C. Atkinson and S. E. Fienberg. ISBN 0 387 96111 9. Springer, New York, 1985. xvi + 606 pp.

D-optimum designs for heteroscedastic linear models

Abstract The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the mathematical foundations differ. The example studied is a second-order two-factor response surface for the mean with a parametric nonlinear variance function. The theory is used both for constructing designs and for checking optimality. A major potential for application is to experimental design in off-line quality control.

Recent Developments in the Methods of Optimum and Related Experimental Designs

Summary A survey is given of recent statistical work on the design of experiments, based on the literature of the last six years. The emphasis is on nonstandard applications of optimum design theory. Reference is made to surveys on the theory of optimum experimental design, crossover designs and incomplete block designs.

Exploratory tools for clustering multivariate data

The forward search provides a series of robust parameter estimates based on increasing numbers of observations. The resulting series of robust Mahalanobis distances is used to cluster multivariate normal data. The method depends on envelopes of the distribution of the test statistics in forward plots. These envelopes can be found by simulation; flexible polynomial approximations to the envelopes are given. New graphical tools provide methods not only of detecting clusters but also of determining their membership. Comparisons are made with mclust and k-means clustering.