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AuthorAtkinson, Anthony. author
TitleRobust Diagnostic Regression Analysis [electronic resource] / by Anthony Atkinson, Marco Riani
ImprintNew York, NY : Springer New York : Imprint: Springer, 2000
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1160-0
Descript XVI, 328 p. online resource

SUMMARY

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 way in which models are fitted, for example, by least squares, we can lose inforยญ mation 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 our book is to combine robustness and a forward" " search through the data with regression diagnostics and computer graphics. We provide easily understood plots that use information from the whole sample to display the effect of each observation on a wide variety of aspects of the fitted model. This bald statement of the contents of our book masks the excitement we feel about the methods we have developed based on the forward search. We are continuously amazed, each time we analyze a new set of data, by the amount of information the plots generate and the insights they provide. We believe our book uses comparatively elementary methods to move regression in a completely new and useful direction. We have written the book to be accessible to students and users of statistical methods, as well as for professional statisticians


CONTENT

1 Some Regression Examples -- 1.1 Influence and Outliers -- 1.2 Three Examples -- 1.3 Checking and Building Models -- 2 Regression and the Forward Search -- 2.1 Least Squares -- 2.2 Added Variables -- 2.3 Deletion Diagnostics -- 2.4 The Mean Shift Outlier Model -- 2.5 Simulation Envelopes -- 2.6 The Forward Search -- 2.7 Further Reading -- 2.8 Exercises -- 2.9 Solutions -- 3 Regression -- 3.1 Hawkinsโ{128}{153} Data -- 3.2 Stack Loss Data -- 3.3 Salinity Data -- 3.4 Ozone Data -- 3.5 Exercises -- 3.6 Solutions -- 4 Transformations to Normality -- 4.1 Background -- 4.2 Transformations in Regression -- 4.3 Wool Data -- 4.4 Poison Data -- 4.5 Modified Poison Data -- 4.6 Doubly Modified Poison Data: An Example of Masking -- 4.7 Multiply Modified Poison Dataโ{128}{148}More Masking -- 4.8 Ozone Data -- 4.9 Stack Loss Data -- 4.10 Musselsโ{128}{153} Muscles: Transformation of the Response -- 4.11 Transforming Both Sides of a Model -- 4.12 Shortleaf Pine -- 4.13 Other Transformations and Further Reading -- 4.14 Exercises -- 4.15 Solutions -- 5 Nonlinear Least Squares -- 5.1 Background -- 5.2 The Forward Search -- 5.3 Radioactivity and Molar Concentration of Nifedipene -- 5.4 Enzyme Kinetics -- 5.5 Calcium Uptake -- 5.6 Nitrogen in Lakes -- 5.7 Isomerization ofn-Pentane -- 5.8 Related Literature -- 5.9 Exercises -- 5.10 Solutions -- 6 Generalized Linear Models -- 6.1 Background -- 6.2 The Exponential Family -- 6.3 Mean, Variance, and Likelihood -- 6.4 Maximum Likelihood Estimation -- 6.5 Inference -- 6.6 Checking Generalized Linear Models -- 6.7 Gamma Models -- 6.8 Car Insurance Data -- 6.9 Dielectric Breakdown Strength -- 6.10 Poisson Models -- 6.11 British Train Accidents -- 6.12 Cellular Differentiation Data -- 6.13 Binomial Models -- 6.14 Blissโ{128}{153}s Beetle Data -- 6.15 Mice with Convulsions -- 6.16 Toxoplasmosis and Rainfall -- 6.17 Binary Data -- 6.18 Theory: The Effect of Perfect Fit and the Arcsine Link -- 6.19 Vasoconstriction Data and Perfect Fit -- 6.20 Chapman Data -- 6.21 Developments and Further Reading -- 6.22 Exercises -- 6.23 Solutions -- A Data -- Author Index


Mathematics Probabilities Statistics Mathematics Probability Theory and Stochastic Processes Statistical Theory and Methods



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