Applied Smoothing Techniques for Data Analysis The Kernel Approach with S-Plus Illustrations

by Bowman, Adrian W; Azzalini, Adelchi

• ISBN13: 9780198523963
• ISBN10: 0198523963
• Format: Hardcover
• Copyright: 1997-11-13
• Publisher: Oxford University Press

Summary

This book describes the use of smoothing techniques in statistics and includes both density estimation and nonparametric regression. Incorporating recent advances, it describes a variety of ways to apply these methods to practical problems. Although the emphasis is on using smoothing techniques to explore data graphically, the discussion also covers data analysis with nonparametric curves, as an extension of more standard parametric models. Intended as an introduction, with a focus on applications rather than on detailed theory, the book will be equally valuable for undergraduate and graduate students in statistics and for a wide range of scientists interested in statistical techniques. The text makes extensive reference to S-Plus, a powerful computing environment for exploring data, and provides many S-Plus functions and example scripts. This material, however, is independent of the main body of text and may be skipped by readers not interested in S-Plus.

Table of Contents

1 Density estimation for exploring data	1	(24)
1.1 Introduction	1	(1)
1.2 Basic ideas	1	(5)
1.3 Density estimation in two dimensions	6	(4)
1.4 Density estimation in three dimensions	10	(2)
1.5 Directional data	12	(2)
1.6 Data with bounded support	14	(3)
1.7 Alternative forms of density estimation	17	(4)
1.7.1 Variable bandwidths	17	(1)
1.7.2 Nearest neighbour methods	18	(1)
1.7.3 Orthogonal series methods	19	(1)
1.7.4 Local likelihood and semiparametric density estimation	20	(1)
1.8 Further reading	21	(1)
Exercises	22	(3)
2 Density estimation for inference	25	(23)
2.1 Introduction	25	(1)
2.2 Basic properties of density estimates	25	(4)
2.3 Confidence and variability bands	29	(2)
2.4 Methods of choosing a smoothing parameter	31	(7)
2.4.1 Optimal smoothing	31	(1)
2.4.2 Normal optimal smoothing	31	(1)
2.4.3 Cross-validation	32	(2)
2.4.4 Plug-in bandwidths	34	(1)
2.4.5 Discussion	34	(4)
2.5 Testing normality	38	(3)
2.6 Normal reference band	41	(1)
2.7 Testing independence	42	(2)
2.8 The bootstrap and density estimation	44	(2)
2.9 Further reading	46	(1)
Exercises	46	(2)
3 Nonparametric regression for exploring data	48	(21)
3.1 Introduction	48	(1)
3.2 Basic ideas	48	(4)
3.3 Nonparametric regression in two dimensions	52	(1)
3.4 Local likelihood and smooth logistic regression	53	(6)
3.5 Estimating quantiles and smoothing survival data	59	(3)
3.6 Variable bandwidths	62	(2)
3.7 Alternative forms of nonparametric regression	64	(3)
3.7.1 Gasser-Muller estimate	64	(1)
3.7.2 Smoothing splines	64	(1)
3.7.3 Orthogonal series and wavelets	65	(1)
3.7.4 Discussion	66	(1)
3.8 Further reading	67	(1)
Exercises	67	(2)
4 Inference with nonparametric regression	69	(17)
4.1 Introduction	69	(1)
4.2 Simple properties	69	(4)
4.3 Estimation of XXX(2)	73	(2)
4.4 Confidence intervals and variability bands	75	(2)
4.5 Choice of smoothing parameters	77	(2)
4.6 Testing for no effect	79	(2)
4.7 A reference band for the no-effect model	81	(1)
4.8 The bootstrap and nonparametric regression	82	(2)
4.9 Further reading	84	(1)
Exercises	84	(2)
5 Checking parametric regression models	86	(21)
5.1 Introduction	86	(1)
5.2 Testing for no effect	86	(5)
5.3 Checking a linear relationship	91	(6)
5.4 The pseudo-likelihood ratio test	97	(7)
5.5 Further reading	104	(1)
Exercises	105	(2)
6 Comparing curves and surfaces	107	(22)
6.1 Introduction	107	(1)
6.2 Comparing density estimates in one dimension	107	(5)
6.3 Relative risk in two dimensions	112	(5)
6.4 Comparing regression curves and surfaces	117	(6)
6.5 Testing for parallel regression curves	123	(3)
6.6 Further reading	126	(1)
Exercises	126	(3)
7 Time series data	129	(21)
7.1 Introduction	129	(1)
7.2 Density estimation	129	(5)
7.3 Conditional densities and conditional means	134	(3)
7.4 Repeated measurements and longitudinal data	137	(6)
7.5 Regression with autocorrelated errors	143	(4)
7.6 Further reading	147	(1)
Exercises	148	(2)
8 An introduction to semiparametric and additive models	150	(19)
8.1 Introduction	150	(1)
8.2 Additive models	150	(10)
8.3 Semiparametric and varying coefficient models	160	(3)
8.4 Generalised additive models	163	(4)
8.5 Further reading	167	(1)
Exercises	167	(2)
A Software	169	(6)
References	175	(12)
Author index	187	(4)
Index	191