Statistical Modeling Using Local Gaussian Approximation
- Length: 458 pages
- Edition: 1
- Language: English
- Publisher: Academic Press
- Publication Date: 2021-10-22
- ISBN-10: 0128158611
- ISBN-13: 9780128158616
- Sales Rank: #0 (See Top 100 Books)
Statistical Modeling using Local Gaussian Approximation extends powerful characteristics of the Gaussian distribution, perhaps, the most well-known and most used distribution in statistics, to a large class of non-Gaussian and nonlinear situations through local approximation. This extension enables the reader to follow new methods in assessing dependence and conditional dependence, in estimating probability and spectral density functions, and in discrimination. Chapters in this release cover Parametric, nonparametric, locally parametric, Dependence, Local Gaussian correlation and dependence, Local Gaussian correlation and the copula, Applications in finance, and more.
Additional chapters explores Measuring dependence and testing for independence, Time series dependence and spectral analysis, Multivariate density estimation, Conditional density estimation, The local Gaussian partial correlation, Regression and conditional regression quantiles, and a A local Gaussian Fisher discriminant.
Cover image Title page Table of Contents Copyright Dedication Biography Preface Chapter 1: Introduction Abstract 1.1. Computer code References Chapter 2: Parametric, nonparametric, locally parametric Abstract 2.1. Introduction 2.2. Parametric density models 2.3. Parametric regression models 2.4. Time series 2.5. Nonparametric density estimation 2.6. Nonparametric regression estimation 2.7. Fighting the curse of dimensionality 2.8. Quantile regression 2.9. Semiparametric models 2.10. Locally parametric References Chapter 3: Dependence Abstract 3.1. Introduction 3.2. Weaknesses of Pearson's ρ 3.3. The copula 3.4. Global dependence functionals and tests of independence 3.5. Test functionals generated by local dependence relationships References Chapter 4: Local Gaussian correlation and dependence Abstract 4.1. Introduction 4.2. Local dependence 4.3. Local Gaussian correlation 4.4. Limit theorems 4.5. Properties 4.6. Examples 4.7. Transforming the marginals: Normalized local correlation 4.8. Some practical considerations 4.9. The p-dimensional case 4.10. Proof of asymptotic results References Chapter 5: Local Gaussian correlation and the copula Abstract 5.1. Introduction 5.2. Local Gaussian correlation for copula models 5.3. Examples 5.4. Recognizing copulas by goodness-of-fit 5.5. A real-data study References Chapter 6: Applications in finance Abstract 6.1. Introduction 6.2. Conditional correlation and the bias problem 6.3. Empirical analysis of dependence of financial returns 6.4. The portfolio allocation problem 6.5. Financial contagion References Chapter 7: Measuring dependence and testing for independence Abstract 7.1. Introduction 7.2. Testing of independence in iid pairs of variables using local correlation functionals 7.3. Testing for serial independence in time series 7.4. Describing nonlinear dependence and tests of independence for two time series 7.5. Proofs References Chapter 8: Time series dependence and spectral analysis Abstract 8.1. Introduction 8.2. Local Gaussian spectral densities 8.3. Visualizations and interpretations References Chapter 9: Multivariate density estimation Abstract 9.1. Introduction 9.2. Description of the estimator 9.3. Asymptotic theory 9.4. Bandwidth selection 9.5. An example 9.6. Investigating performance in the multivariate case 9.7. A more flexible version of the LGDE 9.8. Proofs References Chapter 10: Conditional density estimation Abstract 10.1. Introduction 10.2. Estimating the conditional density 10.3. Asymptotic theory for dependent data 10.4. Examples 10.5. Proof of theorems References Chapter 11: The local Gaussian partial correlation Abstract 11.1. Introduction 11.2. The local Gaussian partial correlation 11.3. Properties 11.4. Estimation of the LGPC by local likelihood 11.5. Asymptotic theory 11.6. Examples 11.7. Testing for conditional independence 11.8. The multivariate LGPC References Chapter 12: Regression and conditional regression quantiles Abstract 12.1. Introduction 12.2. Comparison with additive regression modeling 12.3. Local Gaussian regression estimation 12.4. Asymptotic normality 12.5. Example 12.6. Conditional quantiles 12.7. Proof References Chapter 13: A local Gaussian Fisher discriminant Abstract 13.1. Introduction 13.2. A local Gaussian Fisher discriminant 13.3. Some asymptotics of Bayes risk 13.4. Choice of bandwidth 13.5. Illustrations 13.6. Summary remark References Author index Subject index
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