Applied Nonparametric RegressionCambridge University Press, 1990 - 333 sider 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. |
Innhold
Introduction | 3 |
Basic idea of smoothing | 14 |
Smoothing techniques | 24 |
14 | 54 |
23 | 81 |
The kernel method | 84 |
Exercises | 111 |
30 | 114 |
35 | 157 |
Data sets with outliers | 190 |
Nonparametric regression techniques | 203 |
Looking for special features and qualitative | 217 |
Incorporating parametric components | 232 |
Investigating multiple regression by additive | 257 |
37 | 263 |
A desirable computing environment | 291 |
Bootstrap bands | 118 |
32 | 135 |
Exercises | 137 |
Choosing the smoothing parameter | 147 |
39 | 302 |
References | 305 |
| 325 | |
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ACE algorithm algorithm approximation asymptotically optimal bandwidth h boundary canonical kernels computed confidence intervals consider constant constructed cross-validation curve m(x dashed line defined denotes distribution Engel curves Epanechnikov error bars example Figure Friedman Härdle and Marron higher order kernels Hölder continuous k-NN smooth K₁(x kernel estimator kernel function kernel K(u kernel smoother kernel weights label M-smoother marginal density mean squared error method minimizing Nadaraya-Watson neighborhood nonparametric regression nonparametric smoothing normal optimal bandwidth optimal rate outliers parametric model points pointwise polynomial predictor variable procedure projection pursuit quartic kernel random rate of convergence regression curve regression function resampling residuals response variables sample Section 3.1 selected shows simulated data set smoothing parameter solid line spline spline smoothing STEP stochastic tends to zero Theorem tion transformations values variance vector versus net income weight function weight sequence wild bootstrap workunit X₁ XploRe Y₁