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Author: Marc S. Paolella Publisher: John Wiley & Sons ISBN: 1119417872 Category : Mathematics Languages : en Pages : 584
Book Description
A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided. The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution. Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs.
Author: Marc S. Paolella Publisher: John Wiley & Sons ISBN: 1119417872 Category : Mathematics Languages : en Pages : 584
Book Description
A hands-on approach to statistical inference that addresses the latest developments in this ever-growing field This clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal distribution, and their solutions, are developed in detail. Much emphasis throughout is on non-Gaussian distributions, including details on working with the stable Paretian distribution and fast calculation of the noncentral Student's t. An entire chapter is dedicated to optimization, including development of Hessian-based methods, as well as heuristic/genetic algorithms that do not require continuity, with MATLAB codes provided. The book includes both theory and nontechnical discussions, along with a substantial reference to the literature, with an emphasis on alternative, more modern approaches. The recent literature on the misuse of hypothesis testing and p-values for model selection is discussed, and emphasis is given to alternative model selection methods, though hypothesis testing of distributional assumptions is covered in detail, notably for the normal distribution. Presented in three parts—Essential Concepts in Statistics; Further Fundamental Concepts in Statistics; and Additional Topics—Fundamental Statistical Inference: A Computational Approach offers comprehensive chapters on: Introducing Point and Interval Estimation; Goodness of Fit and Hypothesis Testing; Likelihood; Numerical Optimization; Methods of Point Estimation; Q-Q Plots and Distribution Testing; Unbiased Point Estimation and Bias Reduction; Analytic Interval Estimation; Inference in a Heavy-Tailed Context; The Method of Indirect Inference; and, as an appendix, A Review of Fundamental Concepts in Probability Theory, the latter to keep the book self-contained, and giving material on some advanced subjects such as saddlepoint approximations, expected shortfall in finance, calculation with the stable Paretian distribution, and convergence theorems and proofs.
Author: Jaya P. N. Bishwal Publisher: Springer Nature ISBN: 3031038614 Category : Mathematics Languages : en Pages : 634
Book Description
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Author: Michael Grabchak Publisher: Springer ISBN: 3319249274 Category : Mathematics Languages : en Pages : 127
Book Description
This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.
Author: Robert Adler Publisher: Springer Science & Business Media ISBN: 9780817639518 Category : Mathematics Languages : en Pages : 560
Book Description
Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Gareth W. Peters Publisher: John Wiley & Sons ISBN: 1118909542 Category : Mathematics Languages : en Pages : 667
Book Description
ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distribution approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modeling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Author: Osvaldo A. Martin Publisher: CRC Press ISBN: 1000520048 Category : Computers Languages : en Pages : 420
Book Description
Bayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.
Author: Christian Gouriéroux Publisher: OUP Oxford ISBN: 019152509X Category : Business & Economics Languages : en Pages : 190
Book Description
This book introduces a new generation of statistical econometrics. After linear models leading to analytical expressions for estimators, and non-linear models using numerical optimization algorithms, the availability of high- speed computing has enabled econometricians to consider econometric models without simple analytical expressions. The previous difficulties presented by the presence of integrals of large dimensions in the probability density functions or in the moments can be circumvented by a simulation-based approach. After a brief survey of classical parametric and semi-parametric non-linear estimation methods and a description of problems in which criterion functions contain integrals, the authors present a general form of the model where it is possible to simulate the observations. They then move to calibration problems and the simulated analogue of the method of moments, before considering simulated versions of maximum likelihood, pseudo-maximum likelihood, or non-linear least squares. The general principle of indirect inference is presented and is then applied to limited dependent variable models and to financial series.
Author: Svetlozar T. Rachev Publisher: ISBN: Category : Business & Economics Languages : en Pages : 886
Book Description
This text is a comprehensive treatment of the Asset Pricing Theory, based on the assumption that returns are distributed non-normally. More general models are also considered and the corresponding formulae are derived, and it describes estimation techniques and presents empirical applications.
Author: Eric Jondeau Publisher: Springer Science & Business Media ISBN: 1846286964 Category : Mathematics Languages : en Pages : 541
Book Description
This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.
Author: Dennis D. Boos Publisher: Springer Science & Business Media ISBN: 1461448182 Category : Mathematics Languages : en Pages : 567
Book Description
This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods.
Author: Marc S. Paolella
Author: Marc S. Paolella
Author: Jaya P. N. Bishwal
Author: Michael Grabchak
Author: Robert Adler
Author: Gareth W. Peters
Author: Osvaldo A. Martin
Author: Christian Gouriéroux
Author: Svetlozar T. Rachev
Author: Eric Jondeau
Author: Dennis D. Boos