Kernel Smoothing [Hardcover]

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

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 dlSd