Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus IllustrationsThe book describes the use of smoothing techniques in statistics, including both density estimation and nonparametric regression. Considerable advances in research in this area have been made in recent years. The aim of this text is to describe a variety of ways in which these methods can be applied to practical problems in statistics. The role of smoothing techniques in exploring data graphically is emphasised, but the use of nonparametric curves in drawing conclusions from data, as an extension of more standard parametric models, is also a major focus of the book. Examples are drawn from a wide range of applications. The book is intended for those who seek an introduction to the area, with an emphasis on applications rather than on detailed theory. It is therefore expected that the book will benefit those attending courses at an advanced undergraduate, or postgraduate, level, as well as researchers, both from statistics and from other disciplines, who wish to learn about and apply these techniques in practical data analysis. The text makes extensive reference to S-Plus, as a computing environment in which examples can be explored. S-Plus functions and example scripts are provided to implement many of the techniques described. These parts are, however, clearly separate from the main body of text, and can therefore easily be skipped by readers not interested in S-Plus. |
Contents
1 Density estimation for exploring data | 1 |
2 Density estimation for inference | 25 |
3 Nonparametric regression for exploring data | 48 |
4 Inference with nonparametric regression | 69 |
5 Checking parametric regression models | 86 |
6 Comparing curves and surfaces | 107 |
7 Time series data | 129 |
8 An introduction to semiparametric and additive models | 150 |
Software | 169 |
| 175 | |
Author index | 187 |
| 191 | |
Common terms and phrases
aircraft span data approach approximate assess assumption asymptotic autocorrelation Barrier Reef Barrier Reef data bias bootstrap catch score Chapter component computed constructed contours covariate cross-validation defined denotes density estimate density function depth described in Section design points discussed effect F statistic Figure fitted following S-Plus code graphical groups Hastie and Tibshirani kernel function laryngeal cancer latitude left panel linear model linear regression local linear log scale Log span logistic logit longitude matrix method nonparametric estimate nonparametric regression nonparametric regression curve normal distribution observed optimal smoothing parameter p-value panel of Fig panel shows parameter h parametric model plot produced quadratic quadratic form reconstruct Fig reference band regression function residual sum right panel S-Plus Illustration sample scatterplot simple simulated sm.regression smoothing parameter standard deviation sum of squares Taylor series techniques tephra data test statistic Tibshirani 1990 two-dimensional value of h variability bands variable bandwidth vector weights