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.

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