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.
Inhaltsverzeichnis
Preface xvii
Introduction xix
I.1 Estimation of Functionals of Conditional Distributions xx
I.2 Quantitative Finance xxi
I.3 Visualization xxi
I.4 Literature xxiii
PART I METHODS OF REGRESSION AND CLASSIFICATION
1 Overview of Regression and Classification 3
1.1 Regression 3
1.2 Discrete Response Variable 29
1.3 Parametric Family Regression 33
1.4 Classification 37
1.5 Applications in Quantitative Finance 42
1.6 Data Examples 52
1.7 Data Transformations 53
1.8 Central Limit Theorems 58
1.9 Measuring the Performance of Estimators 61
1.10 Confidence Sets 73
1.11 Testing 75
2 Linear Methods and Extensions 77
2.1 Linear Regression 78
2.2 Varying Coefficient Linear Regression 97
2.3 Generalized Linear and Related Models 102
2.4 Series Estimators 107
2.5 Conditional Variance and ARCH models 111
2.6 Applications in Volatility and Quantile Estimation 115
2.7 Linear Classifiers 124
3 Kernel Methods and Extensions 127
3.1 Regressogram 129
3.2 Kernel Estimator 130
3.3 Nearest Neighborhood Estimator 147
3.4 Classification with Local Averaging 148
3.5 Median Smoothing 151
3.6 Conditional Density Estimators 152
3.7 Conditional Distribution Function Estimation 158
3.8 Conditional Quantile Estimation 160
3.9 Conditional Variance Estimation 162
3.10 Conditional Covariance Estimation 176
3.11 Applications in Risk Management 181
3.12 Applications in Portfolio Selection 205
4 Semiparametric and Structural Models 229
4.1 Single Index Model 230
4.2 Additive Model 234
4.3 Other Semiparametric Models 237
5 Empirical Risk Minimization 241
5.1 Empirical Risk 243
5.2 Local Empirical Risk 247
5.3 Support Vector Machines 257
5.4 Stagewise Methods 259
5.5 Adaptive Regressograms 264
PART II VISUALIZATION
6 Visualization of Data 277
6.1 Scatter Plots 278
6.2 Histogram and Kernel Density Estimator 282
6.3 Dimension Reduction 284
6.4 Observations as Objects 288
7 Visualization of Functions 295
7.1 Slices 296
7.2 Partial Dependence Functions 296
7.3 Reconstruction of Sets 299
7.4 Level Set Trees 303
7.5 Unimodal Densities 326
7.5.1 Probability Content of Level Sets 327
7.5.2 Set Visualization 328
Appendix A: R Tutorial 329
A.1 Data Visualization 329
A.2 Linear Regression 331
A.3 Kernel Regression 332
A.4 Local Linear Regression 341
A.5 Additive Models: Backfitting 344
A.6 Single Index Regression 345
A.7 Forward Stagewise Modeling 347
A.8 Quantile Regression 349
References 351
Author Index 361
Topic Index 365
Über den Autor
JUSSI KLEMELÄ, Ph D, 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.
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