Multivariate Nonparametric Regression and Visualization

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 xviiIntroduction xixI.1 Estimation of Functionals of Conditional Distributions xxI.2 Quantitative Finance xxiI.3 Visualization xxiI.4 Literature xxiiiPART I METHODS OF REGRESSION AND CLASSIFICATION1 Overview of Regression and Classification 31.1 Regression 31.2 Discrete Response Variable 291.3 Parametric Family Regression 331.4 Classification 371.5 Applications in Quantitative Finance 421.6 Data Examples 521.7 Data Transformations 531.8 Central Limit Theorems 581.9 Measuring the Performance of Estimators 611.10 Confidence Sets 731.11 Testing 752 Linear Methods and Extensions 772.1 Linear Regression 782.2 Varying Coefficient Linear Regression 972.3 Generalized Linear and Related Models 1022.4 Series Estimators 1072.5 Conditional Variance and ARCH models 1112.6 Applications in Volatility and Quantile Estimation 1152.7 Linear Classifiers 1243 Kernel Methods and Extensions 1273.1 Regressogram 1293.2 Kernel Estimator 1303.3 Nearest Neighborhood Estimator 1473.4 Classification with Local Averaging 1483.5 Median Smoothing 1513.6 Conditional Density Estimators 1523.7 Conditional Distribution Function Estimation 1583.8 Conditional Quantile Estimation 1603.9 Conditional Variance Estimation 1623.10 Conditional Covariance Estimation 1763.11 Applications in Risk Management 1813.12 Applications in Portfolio Selection 2054 Semiparametric and Structural Models 2294.1 Single Index Model 2304.2 Additive Model 2344.3 Other Semiparametric Models 2375 Empirical Risk Minimization 2415.1 Empirical Risk 2435.2 Local Empirical Risk 2475.3 Support Vector Machines 2575.4 Stagewise Methods 2595.5 Adaptive Regressograms 264PART II VISUALIZATION6 Visualization of Data 2776.1 Scatter Plots 2786.2 Histogram and Kernel Density Estimator 2826.3 Dimension Reduction 2846.4 Observations as Objects 2887 Visualization of Functions 2957.1 Slices 2967.2 Partial Dependence Functions 2967.3 Reconstruction of Sets 2997.4 Level Set Trees 3037.5 Unimodal Densities 3267.5.1 Probability Content of Level Sets 3277.5.2 Set Visualization 328Appendix A: R Tutorial 329A.1 Data Visualization 329A.2 Linear Regression 331A.3 Kernel Regression 332A.4 Local Linear Regression 341A.5 Additive Models: Backfitting 344A.6 Single Index Regression 345A.7 Forward Stagewise Modeling 347A.8 Quantile Regression 349References 351Author Index 361Topic Index 365

“Altogether, the book provides a very nice overview of nonparametric and semiparametric regression methods with interesting applications to problems in quantitative finance.”  (Mathematical Reviews, 1 October 2015)