Synopses & Reviews
A modern approach to statistical learning and its applications through visualization methodsWith 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.
PW Review
Continuing the theme of his 2009 book on density estimation, Klemeläexplains nonparametric and semiparametric methods and visualization tools related to these estimation methods. He writes for students andresearchers in quantitative finance who want to apply statistical methods, and for students and researchers of statistics who want tolearn to apply statistical methods in quantitative finance. He covers an overview of regression and classification, linear andkernel methods and their extensions, semiparametric and structural models, empirical risk minimization, and the visualization of data and functions.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Synopsis
This book uniquely utilizes visualization tools to explain and study statistical learning methods. Covering classification and regression, the book is divided into two parts. First, various visualization methods are introduced and explained. Here, the reader is presented with applications of visualization techniques to learning samples (including projection pursuit, graphical matrices, and parallel coordinate plots) as well as functions, and sets. Next, the author provides a “toolbox” that contains formal definitions of the methods applied in the book and then proceeds to present visualizations of classified learning samples and classified test samples. Visualization methods are applied for the initial exploration of data, to identify the correct type of classifier, and to estimate the best achievable classification error. Once identified, the classifier’s properties, proper uses, and overall performance are demonstrated and measured using visualization methods. Key areas of coverage include linear methods, kernel methods, additive models and trees, boosting, support vector machines, and nearest neighbor methods In addition to providing applications to engineering and biomedicine, the author also uses financial data sets as real data examples to illustrate nonparametric function estimation. The author’s own R software is used throughout to reproduce and modify the book’s computations and research. Readers can duplicate these applications using the software, available via the book’s related Web site.
About the Author
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.
Table of Contents
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