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Smoothing Methods in Statistics
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Smoothing Methods in Statistics

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ISBN-13:
9780387947167
Einband:
Book
Erscheinungsdatum:
28.05.1998
Seiten:
356
Autor:
Jeffrey S. Simonoff
Gewicht:
710 g
Format:
235x155x23 mm
Sprache:
Englisch
Beschreibung:

This book surveys the uses of smoothing methods in statistics. The coverage has an applied focus, and is very broad, including simple and complex univariate and multivariate density estimation, nonparametric regression estimation, categorical data smoothing, and applications of smoothing to other areas of 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.
This book surveys the uses of smoothing methods in statistics. The coverage has an applied focus, and is very broad, including simple and complex univariate and multivariate density estimation, nonparametric regression estimation, categorical data smoothing, and applications of smoothing to other areas of statistics. The book will be of particular interest to data analysts, as arguments generally proceed from actual data rather than statistical theory. The "Background Material" sections will interest statisticians studying the area of smoothing methods. The list of over 750 references allows researchers to find the original sources for more details. The "Computational Issues" sections provide sources for statistical software that implements the discussed methods, including both commercial and non-commercial sources. The book can also be used as a textbook for a course in smoothing. Each chapter includes exercises with a heavily computational focus based upon the data sets used in the book.

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