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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| Hlavní autor: | |
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| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Hoboken N.J
Wiley
2018
John Wiley & Sons John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydání: | 1st ed. |
| Témata: | |
| ISBN: | 9781118456057, 1118890507, 111845605X, 9781118890509 |
| On-line přístup: | Získat plný text |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Ghosh, Sucharita |
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| Notes | Includes bibliographical references (p. 217-242) and indexes |
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| Snippet | Comprehensive theoretical overview of kernel smoothing methods with motivating examples Kernel smoothing is a flexible nonparametric curve estimation method... |
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| SubjectTerms | Kernel functions MATHEMATICS Probability & Statistics Smoothing (Statistics) |
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| Subtitle | principles, methods and applications |
| TableOfContents | 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 |
| Title | Kernel smoothing |
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