Multivariate nonparametric regression and visualization : with R and applications to finance

Title:

Personal Author:

Klemelä, Jussi, 1965-

Series:

Wiley series in computational statistics ; 699

Publication Information:

Hoboken, New Jersey : Wiley-Interscience, 2014

Physical Description:

xxiii, 367 p. : ill. ; 23 cm.

ISBN:

9780470384428

Subject Term:

Finance -- Mathematical models

Visualization

Regression analysis

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010332345	HG176.5 K55 2014	Open Access Book	Book	Searching... Unknown
Searching... PSZ KL	33000000010097	HG176.5 K55 2014	Open Access Book	Book	Searching... Unknown

Summary

A modern approach to statistical learning and its applications through visualization methods

With a unique and innovative presentation, Multivariate Nonparametric Regression and Visualization provides readers with the core statistical concepts to obtain complete and accurate predictions when given a set of data. Focusing on nonparametric methods to adapt to the multiple types of data generating mechanisms, the book begins with an overview of classification and regression.

The book then introduces and examines various tested and proven visualization techniques for learning samples and functions. Multivariate Nonparametric Regression and Visualization identifies risk management, portfolio selection, and option pricing as the main areas in which statistical methods may be implemented in quantitative finance. The book provides coverage of key statistical areas including linear methods, kernel methods, additive models and trees, boosting, support vector machines, and nearest neighbor methods. Exploring the additional applications of nonparametric and semiparametric methods, Multivariate Nonparametric Regression and Visualization features:

An extensive appendix with R-package training material to encourage duplication and modification of the presented computations and research Multiple examples to demonstrate the applications in the field of finance Sections with formal definitions of the various applied methods for readers to utilize throughout the book

Multivariate Nonparametric Regression and Visualization is an ideal textbook for upper-undergraduate and graduate-level courses on nonparametric function estimation, advanced topics in statistics, and quantitative finance. The book is also an excellent reference for practitioners who apply statistical methods in quantitative finance.

Author Notes

JUSSI KLEMELÄ, PhD, is Senior Research Fellow in the Department of Mathematical Sciences at the University of Oulu. He has written numerous journal articles on his research interests, which include density estimation and the implementation of cutting edge visualization tools. Dr. Klemelä is the author of Smoothing of Multivariate Data: Density Estimation and Visualization , also published by Wiley.

Preface	p. xvii
Introduction	p. xix
1.1 Estimation of Functionals of Conditional Distributions	p. xx
1.2 Quantitative Finance	p. xxi
1.3 Visualization	p. xxi
1.4 Literature	p. xxiii
Part I Methods of Regression and Classification
1 Overview of Regression and Classification	p. 3
1.1 Regression	p. 3
1.1.1 Random Design and Fixed Design	p. 4
1.1.2 Mean Regression	p. 5
1.1.3 Partial Effects and Derivative Estimation	p. 8
1.1.4 Variance Regression	p. 9
1.1.5 Covariance and Correlation Regression	p. 13
1.1.6 Qu antile Regression	p. 14
1.1.7 Approximation of the Response Variable	p. 18
1.1.8 Conditional Distribution and Density	p. 21
1.1.9 Time Series Data	p. 23
1.1.10 Stochastic Control	p. 25
1.1.11 Instrumental Variables	p. 26
1.2 Discrete Response Variable	p. 29
1.2.1 Binary Response Models	p. 29
1.2.2 Discrete Choice Models	p. 31
1.2.3 Count Data	p. 33
1.3 Parametric Family Regression	p. 33
1.3.1 General Parametric Family	p. 33
1.3.2 Exponential Family Regression	p. 35
1.3.3 Copula Modeling	p. 36
1.4 Classification	p. 37
1.4.1 Bayes Risk	p. 38
1.4.2 Methods of Classification	p. 39
1.5 Applications in Quantitative Finance	p. 42
1.5.1 Risk Management	p. 42
1.5.2 Variance Trading	p. 44
1.5.3 Portfolio Selection	p. 45
1.5.4 Option Pricing and Hedging	p. 50
1.6 Data Examples	p. 52
1.6.1 Time Series of S&P 500 Returns	p. 52
1.6.2 Vector Time Series of S&P 500 and Nasdaq-100 Returns	p. 53
1.7 Data Transformations	p. 53
1.7.1 Data Sphering	p. 54
1.7.2 Copula Transformation	p. 55
1.7.3 Transformations of the Response Variable	p. 56
1.8 Central Limit Theorems	p. 58
1.8.1 Independent Observations	p. 58
1.8.2 Dependent Observations	p. 58
1.8.3 Estimation of the Asymptotic Variance	p. 60
1.9 Measuring the Performance of Estimators	p. 61
1.9.1 Performance of Regression Function Estimators	p. 61
1.9.2 Performance of Conditional Variance Estimators	p. 66
1.9.3 Performance of Conditional Covariance Estimators	p. 68
1.9.4 Performance of Quantile Function Estimators	p. 69
1.9.5 Performance of Estimators of Expected Shortfall	p. 71
1.9.6 Performance of Classifiers	p. 72
1.10 Confidence Sets	p. 73
1.10.1 Pointwise Confidence Intervals	p. 73
1.10.2 Confidence Bands	p. 75
1.11 Testing	p. 75
2 Linear Methods and Extensions	p. 77
2.1 Linear Regression	p. 78
2.1.1 Least Squares Estimator	p. 79
2.1.2 Generalized Method of Moments Estimator	p. 81
2.1.3 Ridge Regression	p. 84
2.1.4 Asymptotic Distributions for Linear Regression	p. 87
2.1.5 Tests and Confidence Intervals for Linear Regression	p. 90
2.1.6 Variable Selection	p. 92
2.1.7 Applications of Linear Regression	p. 94
2.2 Varying Coefficient Linear Regression	p. 97
2.2.1 The Weighted Least Squares Estimator	p. 97
2.2.2 Applications of Varying Coefficient Regression	p. 98
2.3 Generalized Linear and Related Models	p. 102
2.3.1 Generalized Linear Models	p. 102
2.3.2 Binary Response Models	p. 104
2.3.3 Growth Models	p. 107
2.4 Series Estimators	p. 107
2.4.1 Least Squares Series Estimator	p. 107
2.4.2 Orthonormal Basis Estimator	p. 108
2.4.3 Splines	p. 110
2.5 Conditional Variance and ARCH Models	p. 111
2.5.1 Least Squares Estimator	p. 112
2.5.2 ARCH Model	p. 113
2.6 Applications in Volatility and Quantile Estimation	p. 116
2.6.1 Benchmarks for Quantile Estimation	p. 116
2.6.2 Volatility and Quantiles with the LS Regression	p. 118
2.6.3 Volatility with the Ridge Regression	p. 121
2.6.4 Volatility and Quantiles with ARCH	p. 122
2.7 Linear Classifiers	p. 124
3 Kernel Methods and Extensions	p. 127
3.1 Regressogram	p. 129
3.2 Kernel Estimator	p. 130
3.2.1 Definition of the Kernel Regression Estimator	p. 130
3.2.2 Comparison to the Regressogram	p. 132
3.2.3 Gasser-Müller and Priestley-Chao Estimators	p. 134
3.2.4 Moving Averages	p. 134
3.2.5 Locally Stationary Data	p. 136
3.2.6 Curse of Dimensionality	p. 140
3.2.7 Smoothing Parameter Selection	p. 140
3.2.8 Effective Sample Size	p. 142
3.2.9 Kernel Estimator of Partial Derivatives	p. 145
3.2.10 Confidence Intervals in Kernel Regression	p. 146
3.3 Nearest-Neighbor Estimator	p. 147
3.4 Classification with Local Averaging	p. 148
3.4.1 Kernel Classification	p. 148
3.4.2 Nearest-Neighbor Classification	p. 149
3.5 Median Smoothing	p. 151
3.6 Conditional Density Estimation	p. 152
3.6.1 Kernel Estimator of Conditional Density	p. 152
3.6.2 Histogram Estimator of Conditional Density	p. 156
3.6.3 Nearest-Neighbor Estimator of Conditional Density	p. 157
3.7 Conditional Distribution Function Estimation	p. 158
3.7.1 Local Averag i ng Estimator	p. 159
3.7.2 Time-Space Smoothing	p. 159
3.8 Conditional Quantile Estimation	p. 160
3.9 Conditional Variance Estimation	p. 162
3.9.1 State-Space Smoothing and Variance Estimation	p. 162
3.9.2 Garch and Variance Estimation	p. 163
3.9.3 Moving Averages and Variance Estimation	p. 172
3.10 Conditional Covariance Estimation	p. 176
3.10.1 State-Space Smoothing and Covariance Estimation	p. 178
3.10.2 GARCH and Covariance Estimation	p. 178
3.10.3 Moving Averages and Covariance Estimation	p. 181
3.11 Applications in Risk Management	p. 181
3.11.1 Volatility Estimation	p. 182
3.11.2 Covariance and Correlation Estimation	p. 193
3.11.3 Quantile Estimation	p. 198
3.12 Applications in Portfolio Selection	p. 205
3.12.1 Portfolio Selection Using Regression Functions	p. 205
3.12.2 Portfolio Selection Using Classification	p. 215
3.12.3 Portfolio Selection Using Markowitz Criterion	p. 223
4 Semiparametric and Structural Models	p. 229
4.1 Single-Index Model	p. 230
4.1.1 Definition of the Single-Index Model	p. 230
4.1.2 Estimators in the Single-Index Model	p. 230
4.2 Additive Model	p. 234
4.2.1 Definition of the Additive Model	p. 234
4.2.2 Estimators in the Additive Model	p. 235
4.3 Other Semiparametric Models	p. 237
4.3.1 Partially Linear Model	p. 237
4.3.2 Related Models	p. 238
5 Empirical Risk Minimization	p. 241
5.1 Empirical Risk	p. 243
5.1.1 Conditional Expectation	p. 243
5.1.2 Conditional Quantile	p. 244
5.1.3 Conditional Density	p. 245
5.2 Local Empirical Risk	p. 247
5.2.1 Local Polynomial Estimators	p. 247
5.2.2 Local Likelihood Estimators	p. 255
5.3 Support Vector Machines	p. 257
5.4 Stagewise Methods	p. 259
5.4.1 Forward Stagewise Modeling	p. 259
5.4.2 Stagewise Fitting of Additive Models	p. 261
5.4.3 Projection Pursuit Regression	p. 262
5.5 Adaptive Regressograms	p. 264
5.5.1 Greedy Regressograms	p. 264
5.5.2 CART	p. 268
5.5.3 Dyadic CART	p. 271
5.5.4 Bootstrap Aggregation	p. 272
Part II Visualization
6 Visualization of Data	p. 277
6.1 Scatter Plots	p. 278
6.1.1 Two-Dimensional Scatter Plots	p. 278
6.1.2 One-Dimensional Scatter Plots	p. 278
6.1.3 Three- and Higher-Dimensional Scatter Plots	p. 282
6.2 Histogram and Kernel Density Estimator	p. 283
6.3 Dimension Reduction	p. 284
6.3.1 Projection Pursuit	p. 284
6.3.2 Multidimensional Scaling	p. 286
6.4 Observations as Objects	p. 288
6.4.1 Graphical Matrices	p. 289
6.4.2 Parallel Coordinate Plots	p. 290
6.4.3 Other Methods	p. 293
7 Visualization of Functions	p. 295
7.1 Slices	p. 296
7.2 Partial Dependence Functions	p. 298
7.3 Reconstruction of Sets	p. 299
7.3.1 Estimation of Level Sets of a Function	p. 300
7.3.2 Point Cloud Data	p. 303
7.4 Level Set Trees	p. 304
7.4.1 Definition and Illustrations	p. 304
7.4.2 Calculation of Level Set Trees	p. 308
7.4.3 Volume Function	p. 313
7.4.4 Barycenter Plot	p. 321
7.4.5 Level Set Trees in Regression Function Estimation	p. 322
7.5 Unimodal Densities	p. 325
7.5.1 Probability Content of Level Sets	p. 327
7.5.2 Set Visualization	p. 327
Appendix A R Tutorial	p. 329
A.1 Data Visualization	p. 329
A.1.1 QQ Plots	p. 329
A.1.2 Tail Plots	p. 330
A.1.3 Two-Dimensional Scatter Plots	p. 330
A.1.4 Three-Dimensional Scatter Plots	p. 331
A.2 Linear Regression	p. 331
A.3 Kernel Regression	p. 332
A.3.1 One-Dimensional Kernel Regression	p. 332
A.3.2 Moving Averages	p. 333
A.3.3 wo-Dimensional Kernel Regression	p. 334
A.3.4 hree- and Higher-Dimensional Kernel Regression	p. 336
A.3.5 Kernel Estimator of Derivatives	p. 338
A.3.6 Combined State- and Time-Space Smoothing	p. 340
A.4 Local Linear Regression	p. 341
A.4.1 One-Dimensional Local Linear Regression	p. 341
A.4.2 Two-Dimensional Local Linear Regression	p. 342
A.4.3 Three- and Higher-Dimensional Local Linear Regression	p. 343
A.4.4 Local Linear Derivative Estimation	p. 343
A.5 Additive Models: Backfitting	p. 344
A.6 Single-Index Regression	p. 345
A.6.1 Estimating the Index	p. 346
A.6.2 Estimating the Link Function	p. 346
A.6.3 Plotting the Single-Index Regression Function	p. 346
A.7 Forward Stagewise Modeling	p. 347
A.7.1 Stagewise Fitting of Additive Models	p. 347
A.7.2 Projection Pursuit Regression	p. 348
A.8 Quantile Regression	p. 349
A.8.1 Linear Quantile Regression	p. 349
A.8.2 Kernel Quantile Regression	p. 349
References	p. 351
Author Index	p. 361
Topic Index	p. 365

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Table of Contents