Statistical Modeling Using Local Gaussian Approximation
- 1st Edition - October 5, 2021
- Imprint: Academic Press
- Authors: Dag Tjøstheim, Håkon Otneim, Bård Støve
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 5 8 6 1 - 6
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 5 4 4 5 - 8
Statistical Modeling using Local Gaussian Approximation extends powerful characteristics of the Gaussian distribution, perhaps, the most well-known and most used distribut… Read more
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Request a sales quoteStatistical 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.
- Reviews local dependence modeling with applications to time series and finance markets
- Introduces new techniques for density estimation, conditional density estimation, and tests of conditional independence with applications in economics
- Evaluates local spectral analysis, discovering hidden frequencies in extremes and hidden phase differences
- Integrates textual content with three useful R packages
Graduate students and 1st year PhD students researching problems in econometrics, statistics, financial econometrics and related areas where it is important to model statistical dependence, do density and conditional density estimation, and seek for periodicities and cycles in data
- 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
- Edition: 1
- Published: October 5, 2021
- No. of pages (Paperback): 458
- No. of pages (eBook): 458
- Imprint: Academic Press
- Language: English
- Paperback ISBN: 9780128158616
- eBook ISBN: 9780128154458
DT
Dag Tjøstheim
Dag Tjøstheim is Emeritus Professor, Department of Mathematics, University of Bergen. He has a PhD in applied mathematics from Princeton University (1974). He has authored more than 120 papers in international journals. He is a member of the Norwegian Academy of Sciences and has received several prizes for his scientific work. His main interests are in econometrics, nonlinear time series, nonparametric methods, modeling of dependence, spatial variables, and fishery statistics.
Affiliations and expertise
Emeritus Professor, Department of Mathematics, University of Bergen, NorwayHO
Håkon Otneim
Håkon Otneim is Associate Professor at the Norwegian School of Economics. He has a PhD in statistics from the University of Bergen (2016). He has published papers in international journals about multivariate density estimation and conditional density estimation. His research interests include development and application of non- and semiparametric statistics, statistical programming, and data visualization.
Affiliations and expertise
Norwegian School of Economics, Bergen, NorwayBS
Bård Støve
Bård Støve is Professor of Statistics at the University of Bergen. He received his PhD degree in Statistics, 2005. He was Assistant Professor at the Norwegian School of Economics (2007--2011) and worked as an Actuary in a consulting firm (2005--2007). He has been working on the development of nonparametric models and application of such models to areas in finance and economics. He has published several research papers in journals such as Econometric Theory and Scandinavian Journal of Statistics.
Affiliations and expertise
Associate Professor, Department of Mathematics, University of Bergen, NorwayRead Statistical Modeling Using Local Gaussian Approximation on ScienceDirect