Generalized Additive Models
This book describes an array of power tools for data analysis that are based on nonparametric regression and smoothing techniques. These methods relax the linear assumption of many standard models and allow analysts to uncover structure in the data that might otherwise have been missed. While McCullagh and Nelder's Generalized Linear Models shows how to extend the usual linear methodology to cover analysis of a range of data types, Generalized Additive Models enhances this methodology even further by incorporating the flexibility of nonparametric regression. Clear prose, exercises in each chapter, and case studies enhance this popular text.
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absent ACE algorithm additive fit additive model analysis approximation asymptotic B-splines backfitting algorithm basis functions bias binary bootstrap Chapter components computed concurvity convergence covariance criterion cross-validation cubic smoothing spline cubic spline curves defined degrees of freedom denote derived described deviance diagonal discuss distribution eigenvalues eigenvectors equivalent kernel error estimating equations example Exercise exponential family fitted functions fitted values Gaussian interaction interior knots iterative kernel smoothers kyphosis least-squares likelihood linear model linear regression linear smoothers locally-weighted running-line log-likelihood logistic logistic regression logit M-estimation mean squared error method minimize neighbourhood Newton-Raphson nonlinear nonparametric observations operator optimal ozone partial residuals penalized least-squares plot points pointwise predictor problem regression model regression splines response running-line smoother sample scatterplot scatterplot smoother shows simple simulated smoother matrix smoothing parameter solution span squared standard-error bands surface symmetric tr(SA transformation univariate variance vector virus level Wahba weights zero