Smoothing Methods in Statistics

Springer Science & Business Media, 6 Jun 1996 - 338 halaman
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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Isi

 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 Hak Cipta

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Tentang pengarang (1996)

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.