Kernel smoothing principles, methods and applications
Comprehensive theoretical overview of kernel smoothing methods with motivating examples Kernel smoothing is a flexible nonparametric curve estimation method that is applicable when parametric descriptions of the data are not sufficiently adequate. This book explores theory and methods of kernel smoo...
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| Main Author: | |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
Hoboken N.J
Wiley
2018
John Wiley & Sons John Wiley & Sons, Incorporated Wiley-Blackwell |
| Edition: | 1st ed. |
| Subjects: | |
| ISBN: | 9781118456057, 1118890507, 111845605X, 9781118890509 |
| Online Access: | Get full text |
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Table of Contents:
- Intro -- Kernel Smoothing -- Contents -- Preface -- 1 Density Estimation -- 1.1 Introduction -- 1.1.1 Orthogonal polynomials -- 1.2 Histograms -- 1.2.1 Properties of the histogram -- 1.2.2 Frequency polygons -- 1.2.3 Histogram bin widths -- 1.2.4 Average shifted histogram -- 1.3 Kernel density estimation -- 1.3.1 Naive density estimator -- 1.3.2 Parzen-Rosenblatt kernel density estimator -- 1.3.3 Bandwidth selection -- 1.4 Multivariate density estimation -- 2 Nonparametric Regression -- 2.1 Introduction -- 2.1.1 Method of least squares -- 2.1.2 Influential observations -- 2.1.3 Nonparametric regression estimators -- 2.2 Priestley-Chao regression estimator -- 2.2.1 Weak consistency -- 2.3 Local polynomials -- 2.3.1 Equivalent kernels -- 2.4 Nadaraya-Watson regression estimator -- 2.5 Bandwidth selection -- 2.6 Further remarks -- 2.6.1 Gasser-Müller estimator -- 2.6.2 Smoothing splines -- 2.6.3 Kernel efficiency -- 3 Trend Estimation -- 3.1 Time series replicates -- 3.1.1 Model -- 3.1.2 Estimation of common trend function -- 3.1.3 Asymptotic properties -- 3.2 Irregularly spaced observations -- 3.2.1 Model -- 3.2.2 Derivatives, distribution function, and quantiles -- 3.2.3 Asymptotic properties -- 3.2.4 Bandwidth selection -- 3.3 Rapid change points -- 3.3.1 Model and definition of rapid change -- 3.3.2 Estimation and asymptotics -- 3.4 Nonparametric M-estimation of a trend function -- 3.4.1 Kernel-based M-estimation -- 3.4.2 Local polynomial M-estimation -- 4 Semiparametric Regression -- 4.1 Partial linear models with constant slope -- 4.2 Partial linear models with time-varying slope -- 4.2.1 Estimation -- 4.2.2 Assumptions -- 4.2.3 Asymptotics -- 5 Surface Estimation -- 5.1 Introduction -- 5.2 Gaussian subordination -- 5.3 Spatial correlations -- 5.4 Estimation of the mean and consistency -- 5.4.1 Asymptotics -- 5.5 Variance estimation
- 5.6 Distribution function and spatial Gini index -- 5.6.1 Asymptotics -- References -- Author Index -- Subject Index -- EULA