Applied Nonparametric Regression
Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. Härdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper understanding of the techniques. The methods covered in this text have numerous applications in many areas using statistical analysis. Examples are drawn from economics as well as from other disciplines including medicine and engineering.
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algorithm approximation asymptotically optimal average bandwidth h boundary canonical kernels computed confidence intervals consider constant constructed cross-validation curve m(x dashed line defined denotes density estimation derivative distribution Engel curve Epanechnikov error bars example Family Expenditure Survey Figure fixed design model Gasser Gaussian given Hardle and Marron Hildenbrand k-NN smoother kernel estimator kernel function kernel smoother kernel weights Kh(x label M-smoother marginal density mean squared error mh(x minimizes neighborhood nonparametric regression nonparametric smoothing normal observation errors optimal bandwidth optimal rate outliers parametric model points pointwise polynomial potato versus predictor variable problem procedure projection pursuit quartic kernel random rate of convergence regression curve regression function regressogram residuals response variables sample shows simulated data set smoothing method smoothing parameter smoothing techniques solid line spline smoothing STEP stochastic Table tends to zero Theorem tion transformations values vector versus net income weight function weight sequence wild bootstrap workunit XploRe
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