Smoothing Methods in Statistics

Introduction.- 1.1 Smoothing Methods: a Nonparametric/Parametric Compromise.- 1.2 Uses of Smoothing Methods.- 1.3 Outline of the Chapters.- Background material.- Computational issues.- Exercises.- 2. Simple Univariate Density Estimation.- 2.1 The Histogram.- 2.2 The Frequency Polygon.- 2.3 Varying the Bin Width.- 2.4 The Effectiveness of Simple Density Estimators.- Background material.- Computational issues.- Exercises.- 3. Smoother Univariate Density Estimation.- 3.1 Kernel Density Estimation.- 3.2 Problems with Kernel Density Estimation.- 3.3 Adjustments and Improvements to Kernel Density Estimation.- 3.4 Local Likelihood Estimation.- 3.5 Roughness Penalty and Spline-Based Methods.- 3.6 Comparison of Univariate Density Estimators.- Background material.- Computational issues.- Exercises.- 4. Multivariate Density Estimation.- 4.1 Simple Density Estimation Methods.- 4.2 Kernel Density Estimation.- 4.3 Other Estimators.- 4.4 Dimension Reduction and Projection Pursuit.- 4.5 The State of Multivariate Density Estimation.- Background material.- Computational issues.- Exercises.- 5. Nonparametrie Regression.- 5.1 Scatter Plot Smoothing and Kernel Regression.- 5.2 Local Polynomial Regression.- 5.3 Bandwidth Selection.- 5.4 Locally Varying the Bandwidth.- 5.5 Outliers and Autocorrelation.- 5.6 Spline Smoothing.- 5.7 Multiple Predictors and Additive Models.- 5.8 Comparing Nonparametric Regression Methods.- Background material.- Computational issues.- Exercises.- 6. Smoothing Ordered Categorical Data.- 6.1 Smoothing and Ordered Categorical Data.- 6.2 Smoothing Sparse Multinomials.- 6.3 Smoothing Sparse Contingency Tables.- 6.4 Categorical Data, Regression, and Density Estimation.- Background material.- Computational issues.- Exercises.- 7. Further Applications of Smoothing.- 7.1 Discriminant Analysis.- 7.2 Goodness-of-Fit Tests.- 7.3 Smoothing-Based Parametric Estimation.- 7.4 The Smoothed Bootstrap.- Background material.- Computational issues.- Exercises.- Appendices.- A. Descriptions of the Data Sets.- B. More on Computational Issues.- References.- Author Index.