Multivariate nonparametric regression and visualization with R and applications to finance.
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...
Uložené v:
| Hlavný autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | English |
| Vydavateľské údaje: |
Hoboken, New Jersey
WILEY
2014
Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
| Vydanie: | 1 |
| Edícia: | Wiley series in computational statistics |
| Predmet: | |
| ISBN: | 9781118838044, 9780470384428, 1118838041, 0470384425, 9781118593509, 1118593502 |
| On-line prístup: | Získať plný text |
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- Multivariate nonparametric regression and visualization : with R and applications to finance -- Dedication -- Contents -- Preface -- Introduction -- Part I: Methods of Regression and Classification -- Chapter 1: Overview of Regression and Classification -- Chapter 2: Linear Methods and Extensions -- Chapter 3: Kernel Methods and Extensions -- Chapter 4: Semiparametric and Structural Models -- Chapter 5: Empirical Risk Minimization -- Chapter Part II: Visualization -- Chapter 6: Visualization of Data -- Chapter 7: Visualization of Functions -- Appendix A: R Tutorial -- References -- Author Index -- Topic Index
- 5.3 Support Vector Machines -- 5.4 Stagewise Methods -- 5.4.1 Forward Stagewise Modeling -- 5.4.2 Stagewise Fitting of Additive Models -- 5.4.3 Projection Pursuit Regression -- 5.5 Adaptive Regressograms -- 5.5.1 Greedy Regressograms -- 5.5.2 CART -- 5.5.3 Dyadic CART -- 5.5.4 Bootstrap Aggregation -- PART II VISUALIZATION -- 6 Visualization of Data -- 6.1 Scatter Plots -- 6.1.1 Two-Dimensional Scatter Plots -- 6.1.2 One-Dimensional Scatter Plots -- 6.1.3 Three- and Higher-Dimensional Scatter Plots -- 6.2 Histogram and Kernel Density Estimator -- 6.3 Dimension Reduction -- 6.3.1 Projection Pursuit -- 6.3.2 Multidimensional Scaling -- 6.4 Observations as Objects -- 6.4.1 Graphical Matrices -- 6.4.2 Parallel Coordinate Plots -- 6.4.3 Other Methods -- 7 Visualization of Functions -- 7.1 Slices -- 7.2 Partial Dependence Functions -- 7.3 Reconstruction of Sets -- 7.3.1 Estimation of Level Sets of a Function -- 7.3.2 Point Cloud Data -- 7.4 Level Set Trees -- 7.4.1 Definition and Illustrations -- 7.4.2 Calculation of Level Set Trees -- 7.4.3 Volume Function -- 7.4.4 Barycenter Plot -- 7.4.5 Level Set Trees in Regression Function Estimation -- 7.5 Unimodal Densities -- 7.5.1 Probability Content of Level Sets -- 7.5.2 Set Visualization -- Appendix A: R Tutorial -- A.1 Data Visualization -- A.1.1 QQ Plots -- A.1.2 Tail Plots -- A.1.3 Two-Dimensional Scatter Plots -- A.1.4 Three- Dimensional Scatter Plots -- A.2 Linear Regression -- A.3 Kernel Regression -- A.3.1 One-Dimensional Kernel Regression -- A.3.2 Moving Averages -- A.3.3 Two-Dimensional Kernel Regression -- A.3.4 Three- and Higher-Dimensional Kernel Regression -- A.3.5 Kernel Estimator of Derivatives -- A.3.6 Combined State- and Time-Space Smoothing -- A.4 Local Linear Regression -- A.4.1 One-Dimensional Local Linear Regression -- A.4.2 Two-Dimensional Local Linear Regression
- A.4.3 Three- and Higher-Dimensional Local Linear Regression -- A.4.4 Local Linear Derivative Estimation -- A.5 Additive Models: Backfitting -- A.6 Single-Index Regression -- A.6.1 Estimating the Index -- A.6.2 Estimating the Link Function -- A.6.3 Plotting the Single-Index Regression Function -- A.7 Forward Stagewise Modeling -- A.7.1 Stagewise Fitting of Additive Models -- A.7.2 Projection Pursuit Regression -- A.8 Quantile Regression -- A.8.1 Linear Quantile Regression -- A.8.2 Kernel Quantile Regression -- References -- Author Index -- Topic Index -- EULA
- Cover -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Introduction -- I.1 Estimation of Functionals of Conditional Distributions -- I.2 Quantitative Finance -- I.3 Visualization -- I.4 Literature -- PART I METHODS OF REGRESSION AND CLASSIFICATION -- 1 Overview of Regression and Classification -- 1.1 Regression -- 1.1.1 Random Design and Fixed Design -- 1.1.2 Mean Regression -- 1.1.3 Partial Effects and Derivative Estimation -- 1.1.4 Variance Regression -- 1.1.5 Covariance and Correlation Regression -- 1.1.6 Quantile Regression -- 1.1.7 Approximation of the Response Variable -- 1.1.8 Conditional Distribution and Density -- 1.1.9 Time Series Data -- 1.1.10 Stochastic Control -- 1.1.11 Instrumental Variables -- 1.2 Discrete Response Variable -- 1.2.1 Binary Response Models -- 1.2.2 Discrete Choice Models -- 1.2.3 Count Data -- 1.3 Parametric Family Regression -- 1.3.1 General Parametric Family -- 1.3.2 Exponential Family Regression -- 1.3.3 Copula Modeling -- 1.4 Classification -- 1.4.1 Bayes Risk -- 1.4.2 Methods of Classification -- 1.5 Applications in Quantitative Finance -- 1.5.1 Risk Management -- 1.5.2 Variance Trading -- 1.5.3 Portfolio Selection -- 1.5.4 Option Pricing and Hedging -- 1.6 Data Examples -- 1.6.1 Time Series of S& -- P 500 Returns -- 1.6.2 Vector Time Series of S& -- P 500 and Nasdaq-100 Returns -- 1.7 Data Transformations -- 1.7.1 Data Sphering -- 1.7.2 Copula Transformation -- 1.7.3 Transformations of the Response Variable -- 1.8 Central Limit Theorems -- 1.8.1 Independent Observations -- 1.8.2 Dependent Observations -- 1.8.3 Estimation of the Asymptotic Variance -- 1.9 Measuring the Performance of Estimators -- 1.9.1 Performance of Regression Function Estimators -- 1.9.2 Performance of Conditional Variance Estimators -- 1.9.3 Performance of Conditional Covariance Estimators
- 1.9.4 Performance of Quantile Function Estimators -- 1.9.5 Performance of Estimators of Expected Shortfall -- 1.9.6 Performance of Classifiers -- 1.10 Confidence Sets -- 1.10.1 Pointwise Confidence Intervals -- 1.10.2 Confidence Bands -- 1.11 Testing -- 2 Linear Methods and Extensions -- 2.1 Linear Regression -- 2.1.1 Least Squares Estimator -- 2.1.2 Generalized Method of Moments Estimator -- 2.1.3 Ridge Regression -- 2.1.4 Asymptotic Distributions for Linear Regression -- 2.1.5 Tests and Confidence Intervals for Linear Regression -- 2.1.6 Variable Selection -- 2.1.7 Applications of Linear Regression -- 2.2 Varying Coefficient Linear Regression -- 2.2.1 The Weighted Least Squares Estimator -- 2.2.2 Applications of Varying Coefficient Regression -- 2.3 Generalized Linear and Related Models -- 2.3.1 Generalized Linear Models -- 2.3.2 Binary Response Models -- 2.3.3 Growth Models -- 2.4 Series Estimators -- 2.4.1 Least Squares Series Estimator -- 2.4.2 Orthonormal Basis Estimator -- 2.4.3 Splines -- 2.5 Conditional Variance and ARCH Models -- 2.5.1 Least Squares Estimator -- 2.5.2 ARCH Model -- 2.6 Applications in Volatility and Quantile Estimation -- 2.6.1 Benchmarks for Quantile Estimation -- 2.6.2 Volatility and Quantiles with the LS Regression -- 2.6.3 Volatility with the Ridge Regression -- 2.6.4 Volatility and Quantiles with ARCH -- 2.7 Linear Classifiers -- 3 Kernel Methods and Extensions -- 3.1 Regressogram -- 3.2 Kernel Estimator -- 3.2.1 Definition of the Kernel Regression Estimator -- 3.2.2 Comparison to the Regressogram -- 3.2.3 Gasser-Müller and Priestley-Chao Estimators -- 3.2.4 Moving Averages -- 3.2.5 Locally Stationary Data -- 3.2.6 Curse of Dimensionality -- 3.2.7 Smoothing Parameter Selection -- 3.2.8 Effective Sample Size -- 3.2.9 Kernel Estimator of Partial Derivatives -- 3.2.10 Confidence Intervals in Kernel Regression
- 3.3 Nearest-Neighbor Estimator -- 3.4 Classification with Local Averaging -- 3.4.1 Kernel Classification -- 3.4.2 Nearest-Neighbor Classification -- 3.5 Median Smoothing -- 3.6 Conditional Density Estimation -- 3.6.1 Kernel Estimator of Conditional Density -- 3.6.2 Histogram Estimator of Conditional Density -- 3.6.3 Nearest-Neighbor Estimator of Conditional Density -- 3.7 Conditional Distribution Function Estimation -- 3.7.1 Local Averaging Estimator -- 3.7.2 Time-Space Smoothing -- 3.8 Conditional Quantile Estimation -- 3.9 Conditional Variance Estimation -- 3.9.1 State-Space Smoothing and Variance Estimation -- 3.9.2 GARCH and Variance Estimation -- 3.9.3 Moving Averages and Variance Estimation -- 3.10 Conditional Covariance Estimation -- 3.10.1 State-Space Smoothing and Covariance Estimation -- 3.10.2 GARCH and Covariance Estimation -- 3.10.3 Moving Averages and Covariance Estimation -- 3.11 Applications in Risk Management -- 3.11.1 Volatility Estimation -- 3.11.2 Covariance and Correlation Estimation -- 3.11.3 Quantile Estimation -- 3.12 Applications in Portfolio Selection -- 3.12.1 Portfolio Selection Using Regression Functions -- 3.12.2 Portfolio Selection Using Classification -- 3.12.3 Portfolio Selection Using Markowitz Criterion -- 4 Semiparametric and Structural Models -- 4.1 Single-Index Model -- 4.1.1 Definition of the Single-Index Model -- 4.1.2 Estimators in the Single-Index Model -- 4.2 Additive Model -- 4.2.1 Definition of the Additive Model -- 4.2.2 Estimators in the Additive Model -- 4.3 Other Semiparametric Models -- 4.3.1 Partially Linear Model -- 4.3.2 Related Models -- 5 Empirical Risk Minimization -- 5.1 Empirical Risk -- 5.1.1 Conditional Expectation -- 5.1.2 Conditional Quantile -- 5.1.3 Conditional Density -- 5.2 Local Empirical Risk -- 5.2.1 Local Polynomial Estimators -- 5.2.2 Local Likelihood Estimators
- Intro -- Half Title page -- Title page -- Copyright page -- Dedication -- Preface -- Introduction -- I.1 Estimation of Functionals of Conditional Distributions -- I.2 Quantitative Finance -- I.3 Visualization -- I.4 Literature -- Part I: Methods of Regression and Classification -- Chapter 1: Overview of Regression and Classification -- 1.1 Regression -- 1.2 Discrete Response Variable -- 1.3 Parametric Family Regression -- 1.4 Classification -- 1.5 Applications in Quantitative Finance -- 1.6 Data Examples -- 1.7 Data Transformations -- 1.8 Central Limit Theorems -- 1.9 Measuring the Performance of Estimators -- 1.10 Confidence Sets -- 1.11 Testing -- Chapter 2: Linear Methods and Extensions -- 2.1 Linear Regression -- 2.2 Varying Coefficient Linear Regression -- 2.3 Generalized Linear and Related Models -- 2.4 Series Estimators -- 2.5 Conditional Variance and ARCH Models -- 2.6 Applications in Volatility and Quantile Estimation -- 2.7 Linear Classifiers -- Chapter 3: Kernel Methods and Extensions -- 3.1 Regressogram -- 3.2 Kernel Estimator -- 3.3 Nearest-Neighbor Estimator -- 3.4 Classification with Local Averaging -- 3.5 Median Smoothing -- 3.6 Conditional Density Estimation -- 3.7 Conditional Distribution Function Estimation -- 3.8 Conditional Quantile Estimation -- 3.9 Conditional Variance Estimation -- 3.10 Conditional Covariance Estimation -- 3.11 Applications in Risk Management -- 3.12 Applications in Portfolio Selection -- Chapter 4: Semiparametric and Structural Models -- 4.1 Single-Index Model -- 4.2 Additive Model -- 4.3 Other Semiparametric Models -- Chapter 5: Empirical Risk Minimization -- 5.1 Empirical Risk -- 5.3 Support Vector Machines -- 5.4 Stagewise Methods -- 5.5 Adaptive Regressograms -- Part II: Visualization -- Chapter 6: Visualization of Data -- 6.1 Scatter Plots -- 6.2 Histogram and Kernel Density Estimator
- 6.3 Dimension Reduction -- 6.4 Observations as Objects -- Chapter 7: Visualization of Functions -- 7.1 Slices -- 7.2 Partial Dependence Functions -- 7.3 Reconstruction of Sets -- 7.4 Level Set Trees -- 7.5 Unimodal Densities -- Appendix A: R Tutorial -- A.1 Data Visualization -- A.2 Linear Regression -- A.3 Kernel Regression -- A.4 Local Linear Regression -- A.5 Additive Models: Backfitting -- A.6 Single-Index Regression -- A.7 Forward Stagewise Modeling -- A.8 Quantile Regression -- References -- Author Index -- Topic Index