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 smoothing in a variety of contexts, considering independent and correlated data e.g. with short-memory and long-memory correlations, as well as non-Gaussian data that are transformations of latent Gaussian processes. These types of data occur in many fields of research, e.g. the natural and the environmental sciences, and others. Nonparametric density estimation, nonparametric and semiparametric regression, trend and surface estimation in particular for time series and spatial data and other topics such as rapid change points, robustness etc. are introduced alongside a study of their theoretical properties and optimality issues, such as consistency and bandwidth selection.
Addressing a variety of topics, Kernel Smoothing: Principles, Methods and Applications offers a user-friendly presentation of the mathematical content so that the reader can directly implement the formulas using any appropriate software. The overall aim of the book is to describe the methods and their theoretical backgrounds, while maintaining an analytically simple approach and including motivating examples—making it extremely useful in many sciences such as geophysics, climate research, forestry, ecology, and other natural and life sciences, as well as in finance, sociology, and engineering.
- A simple and analytical description of kernel smoothing methods in various contexts
- Presents the basics as well as new developments
- Includes simulated and real data examples
Kernel Smoothing: Principles, Methods and Applications is a textbook for senior undergraduate and graduate students in statistics, as well as a reference book for applied statisticians and advanced researchers.
| Preface |
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ix | |
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1 | (58) |
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1 | (7) |
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1.1.1 Orthogonal polynomials |
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2 | (6) |
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8 | (11) |
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1.2.1 Properties of the histogram |
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9 | (5) |
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14 | (1) |
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1.2.3 Histogram bin widths |
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15 | (4) |
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1.2.4 Average shifted histogram |
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19 | (1) |
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1.3 Kernel density estimation |
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19 | (34) |
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1.3.1 Naive density estimator |
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21 | (4) |
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1.3.2 Parzen---Rosenblatt kernel density estimator |
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25 | (18) |
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1.3.3 Bandwidth selection |
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43 | (10) |
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1.4 Multivariate density estimation |
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53 | (6) |
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2 Nonparametric Regression |
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59 | (46) |
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59 | (14) |
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2.1.1 Method of least squares |
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60 | (10) |
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2.1.2 Influential observations |
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70 | (1) |
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2.1.3 Nonparametric regression estimators |
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71 | (2) |
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2.2 Priestley---Chao regression estimator |
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73 | (7) |
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77 | (3) |
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80 | (7) |
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84 | (3) |
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2.4 Nadaraya---Watson regression estimator |
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87 | (6) |
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93 | (6) |
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99 | (6) |
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2.6.1 Gasser--Muller estimator |
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99 | (1) |
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100 | (3) |
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103 | (2) |
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105 | (52) |
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3.1 Time series replicates |
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105 | (15) |
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111 | (3) |
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3.1.2 Estimation of common trend function |
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114 | (1) |
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3.1.3 Asymptotic properties |
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114 | (6) |
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3.2 Irregularly spaced observations |
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120 | (21) |
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122 | (3) |
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3.2.2 Derivatives, distribution function, and quantiles |
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125 | (4) |
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3.2.3 Asymptotic properties |
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129 | (8) |
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3.2.4 Bandwidth selection |
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137 | (4) |
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141 | (8) |
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3.3.1 Model and definition of rapid change |
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144 | (1) |
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3.3.2 Estimation and asymptotics |
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145 | (4) |
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3.4 Nonparametric M-estimation of a trend function |
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149 | (8) |
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3.4.1 Kernel-based M-estimation |
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149 | (5) |
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3.4.2 Local polynomial M-estimation |
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154 | (3) |
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4 Semiparametric Regression |
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157 | (24) |
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4.1 Partial linear models with constant slope |
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157 | (3) |
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4.2 Partial linear models with time-varying slope |
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160 | (21) |
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165 | (1) |
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166 | (5) |
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171 | (10) |
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181 | (36) |
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181 | (612) |
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5.2 Gaussian subordination |
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193 | (2) |
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195 | (2) |
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5.4 Estimation of the mean and consistency |
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197 | (6) |
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197 | (6) |
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203 | (3) |
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5.6 Distribution function and spatial Gini Index |
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206 | (11) |
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213 | (4) |
| References |
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217 | (26) |
| Author Index |
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243 | (8) |
| Subject Index |
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251 | |
Sucharita Ghosh, PhD, is a statistician at the Swiss Federal Research Institute WSL, Switzerland. She also teaches graduate level Statistics in the Department of Mathematics, Swiss Federal Institute of Technology in Zurich. She obtained her doctorate in Statistics from the University of Toronto, Masters from the Indian Statistical Institute and B.Sc. from Presidency College, University of Calcutta, India. She was a Statistics faculty member at Cornell University and has held various short-term and long-term visiting faculty positions at universities such as the University of North Carolina at Chapel Hill and University of York, UK. She has also taught Statistics to undergraduate and graduate students at a number of universities, namely in Canada (Toronto), USA (Cornell, UNC Chapel Hill), UK (York), Germany (Konstanz) and Switzerland (ETH Zurich). Her research interests include smoothing, integral transforms, time series and spatial data analysis, having applications in a number of areas including the natural sciences, finance and medicine among others.
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