Smoothing methods in statistics

Jeffrey S. Simonoff0387947167, 9780387947167

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. “It is an excellent reference to the field and has no rival in terms of accessibility, coverage, and utility.” –Journal of the American Statistical Association “This book provides an excellent overview of smoothing methods and concepts, presenting material in an intuitive manner with many interesting graphics…This book provides a handy reference for practicing statisticians and other data analysts. In addition, it is well organized as a classroom textbook.” –Technometrics

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Table of contents :
Contents……Page 9
Preface……Page 6
1.1 Smoothing Methods: a Nonparametric/Parametric Compromise……Page 11
1.2 Uses of Smoothing Methods……Page 18
1.3 Outline of the Chapters……Page 20
Computational issues……Page 21
Exercises……Page 22
2.1 The Histogram……Page 23
2.2 The Frequency Polygon……Page 30
2.3 Varying the Bin Width……Page 32
2.4 The Effectiveness of Simple Density Estimators……Page 36
Background material……Page 39
Computational issues……Page 46
Exercises……Page 47
3.1 Kernel Density Estimation……Page 49
3 2 Problems with Kernel Density Estimation……Page 58
3.3 Adjustments and Improvements to Kernel Density Estimation……Page 62
3.4 Local Likelihood Estimation……Page 73
3.5 Roughness Penalty and Spline-Based Methods……Page 76
3.6 Comparison of Univariate Density Estimators……Page 79
Background material……Page 81
Computational issues……Page 101
Exercises……Page 103
4.1 Simple Density Estimation Methods……Page 105
4.2 Kernel Density Estimation……Page 111
4.3 Other Estimators……Page 120
4.4 Dimension Reduction and Projection Pursuit……Page 126
4 5 The State of Multivariate Density Estimation……Page 130
Background material……Page 132
Computational issues……Page 140
Exercises……Page 141
5.1 Scatter Plot Smoothing and Kernel Regression……Page 143
5.2 Local Polynomial Regression……Page 147
5.3 Bandwidth Selection……Page 160
5 4 Locally Varying the Bandwidth……Page 163
5 5 Outliers and Autocorrelation……Page 169
5.6 Spline Smoothing……Page 177
5.1 Multiple Predictors and Additive Models……Page 187
5 8 Comparing Nonparametric Regression Methods……Page 199
Background material……Page 200
Computational issues……Page 219
Exercises……Page 221
6.1 Smoothing and Ordered Categorical Data……Page 224
6.2 Smoothing Sparse Multinomials……Page 226
6.3 Smoothing Sparse Contingency Tables……Page 235
6.4 Categorical Data, Regression, and Density Estimation……Page 245
Background material……Page 252
Exercises……Page 259
7.1 Discriminant Analysis……Page 261
7.2 Goodness-of-Fit Tests……Page 267
7.3 Smoothing-Based Parametric Estimation……Page 270
7.4 The Smoothed Bootstrap……Page 275
Background material……Page 277
Exercises……Page 282
A. Descriptions of the Data Sets……Page 284
B. More on Computational Issues……Page 297
References……Page 299
Author Index……Page 330
Subject Index……Page 338