Kernel smoothing : principles, methods and applications
著者
書誌事項
Kernel smoothing : principles, methods and applications
John Wiley & Sons, 2018
- hbk
大学図書館所蔵 全4件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 217-242) and indexes
内容説明・目次
内容説明
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.
目次
Preface ix
Density Estimation 1
1.1 Introduction 1
1.1.1 Orthogonal polynomials 2
1.2 Histograms 8
1.2.1 Properties of the histogram 9
1.2.2 Frequency polygons 14
1.2.3 Histogram bin widths 15
1.2.4 Average shifted histogram 19
1.3 Kernel density estimation 19
1.3.1 Naive density estimator 21
1.3.2 Parzen-Rosenblatt kernel density estimator 25
1.3.3 Bandwidth selection 43
1.4 Multivariate density estimation 53
Nonparametric Regression 59
2.1 Introduction 59
2.1.1 Method of least squares 60
2.1.2 Influential observations 70
2.1.3 Nonparametric regression estimators 71
2.2 Priestley-Chao regression estimator 73
2.2.1 Weak consistency 77
2.3 Local polynomials 80
2.3.1 Equivalent kernels 84
2.4 Nadaraya-Watson regression estimator 87
2.5 Bandwidth selection 93
2.6 Further remarks 99
2.6.1 Gasser-Muller estimator 99
2.6.2 Smoothing splines 100
2.6.3 Kernel efficiency 103
Trend Estimation 105
3.1 Time series replicates 105
3.1.1 Model 111
3.1.2 Estimation of common trend function 114
3.1.3 Asymptotic properties 114
3.2 Irregularly spaced observations 120
3.2.1 Model 122
3.2.2 Derivatives, distribution function, and quantiles 125
3.2.3 Asymptotic properties 129
3.2.4 Bandwidth selection 137
3.3 Rapid change points 141
3.3.1 Model and definition of rapid change 144
3.3.2 Estimation and asymptotics 145
3.4 Nonparametric M-estimation of a trend function 149
3.4.1 Kernel-based M-estimation 149
3.4.2 Local polynomial M-estimation 154
Semiparametric Regression 157
4.1 Partial linear models with constant slope 157
4.2 Partial linear models with time-varying slope 160
4.2.1 Estimation 165
4.2.2 Assumptions 166
4.2.3 Asymptotics 171
Surface Estimation 181
5.1 Introduction 181
5.2 Gaussian subordination 193
5.3 Spatial correlations 195
5.4 Estimation of the mean and consistency 197
5.4.1 Asymptotics 197
5.5 Variance estimation 203
5.6 Distribution function and spatial Gini index 206
5.6.1 Asymptotics 213
References 217
Author Index 243
Subject Index 251
「Nielsen BookData」 より