Smoothing Methods in Statistics

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Springer Science & Business Media, 6 Jun 1996 - 338 halaman
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The existence of high speed, inexpensive computing has made it easy to look at data in ways that were once impossible. Where once a data analyst was forced to make restrictive assumptions before beginning, the power of the computer now allows great freedom in deciding where an analysis should go. One area that has benefited greatly from this new freedom is that of non parametric density, distribution, and regression function estimation, or what are generally called smoothing methods. Most people are familiar with some smoothing methods (such as the histogram) but are unlikely to know about more recent developments that could be useful to them. If a group of experts on statistical smoothing methods are put in a room, two things are likely to happen. First, they will agree that data analysts seriously underappreciate smoothing methods. Smoothing meth ods use computing power to give analysts the ability to highlight unusual structure very effectively, by taking advantage of people's abilities to draw conclusions from well-designed graphics. Data analysts should take advan tage of this, they will argue.
 

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Introduction
1
12 Uses of Smoothing Methods
8
13 Outline of the Chapters
10
Background material
11
Exercises
12
Simple Univariate Density Estimation
13
22 The Frequency Polygon
20
23 Varying the Bin Width
22
Nonparametric Regression
134
52 Local Polynomial Regression
138
53 Bandwidth Selection
151
54 Locally Varying the Bandwidth
154
55 Outliers and Autocorrelation
160
56 Spline Smoothing
168
57 Multiple Predictors and Additive Models
178
58 Comparing Nonparametric Regression Methods
190

24 The Effectiveness of Simple Density Estimators
26
Background material Section 21
30
Computational issues
37
Exercises
38
Smoother Univariate Density Estimation
40
32 Problems with Kernel Density Estimation
49
33 Adjustments and Improvements to Kernel Density Estimation
53
34 Local Likelihood Estimation
64
35 Roughness Penalty and SplineBased Methods
67
36 Comparison of Univariate Density Estimators
70
Background material
72
Computational issues
92
Exercises
94
Multivariate Density Estimation
96
42 Kernel Density Estimation
102
43 Other Estimators
111
44 Dimension Reduction and Projection Pursuit
117
45 The State of Multivariate Density Estimation
121
Background material Section 41
123
Computational issues
131
Exercises
132
Background material Section 51
191
Computational issues
210
Exercises
212
Smoothing Ordered Categorical Data
215
62 Smoothing Sparse Multinomials
217
63 Smoothing Sparse Contingency Tables
226
64 Categorical Data Regression and Density Estimation
236
Background material Section 61
243
Computational issues
250
Further Applications of Smoothing
252
72 GoodnessofFit Tests
258
73 SmoothingBased Parametric Estimation
261
74 The Smoothed Bootstrap
266
Background material Section 71
268
Computational issues
273
Appendices
275
B More on Computational Issues
288
References
290
Author Index
321
Subject Index
329
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Jeffrey S. Simonoff is Professor of Statistics at the NYU Stern School of Business. He is a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute. He is author or coauthor of roughly 100 articles and five books on the theory and applications of statistics.

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