Smoothing Methods in Statistics

1. 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. Language: English