Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets.The basic principle is that local averaging or smoothing is performed with respect to a kernel function.
This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilitated by the authors' focus on the simplest settings, namely density estimation and nonparametric regression.
They pay particular attention to the problem of choosing the smoothing parameter of a kernel smoother, and also treat the multivariate case in detail.
Kernel Smoothing is self-contained and assumes only a basic knowledge of statistics, calculus, and matrix algebra. It is an invaluable introduction to the main ideas of kernel estimation for students and researchers from other discipline and provides a comprehensive reference for those familiar with the topic.
More information on the book, and the accompanying R package can be found here.
Preface
Introduction
Introduction
Density estimation and histograms
About this book
Options for reading this book
Bibliographical notes
Univariate kernel density estimation
Introduction
The univariate kernel density estimator
The MSE and MISE criteria
Order and asymptotic notation; Taylor expansion
Order and asymptotic notation
Taylor expansion
Asymptotic MSE and MISE approximations
Exact MISE calculations
Canonical kernels and optimal kernel theory
Higher-older kernels
Measuring how difficult a density is to estimate
Modifications of the kernel density estimations
Local kernel density estimators
Variable kernel density estimators
Transformation kernel density estimators
Density estimation at boundaries
Density derivative estimation
Bibliographical notes
Exercises
Bandwidth selection
Introduction
Quick and simple bandwidth selectors
Normal scale rules
Oversmoothed bandwidth selection rules
Least squares cross-validation
Biased cross-validation
Estimation of density functionals
Plug-in bandwidth selection
Direct plug in rules
Solve-the-equation rules
Smoothed cross-validation bandwidth selection
Comparison of bandwidth selection
Theoretical performance
Practical advice
Bibliographical notes
Exercises
Multivariate kernel density estimation
Introduction
The multivariate kernel density estimator
Asymptotic MISE approximations
Exact MISE calculations
Choice of multivariate kernel
Choice of smoothing parametrisation
Bandwidth selection
Bibliographical notes
Exercises
Kernel regression
Introduction
Local polynomial kernel estimators
Asymptotic MSE approximations: linear case
Fixed equally spaced design
Random design
Asymptotic MSE approximations: general case
Behaviour near the boundary
Comparison with other kernel estimators
Asymptotic comparison
Effective kernels
Derivative estimation
Bandwidth selection
Multivariate nonparametric regression
Bibliographical notes
Exercises
Selected extra topics
Introduction
Kernel density estimation in other settings
Dependent data
Length biased data
Right-censored data
Data measured with error
Hazard function estimation
Spectral density estimation
Likelihood-based regression models
Intensity function estimation
Bibliographical notes
Exercises
Appendixes
A Notation
B Tables
C Facts about normal densities
C.1 Univariate normal densities
C.2 Multivariate normal densities
C.3 Bibliographical notes
D Computation of kernel estimators
D.1 Introduction
D.2 The binned kernel density estimator
D.3 Computation of kernel functional estimates
D.4 Computation of kernel regression estimates
D.5 Extension to multivariate kernel smoothing
D.6 Computing practicalities
D.7 Bibliographical notes
References
Index
Biography
M.P. Wand, M.C. Jones
