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Estimation Of Stable Distributions By Indirect Inference
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Book Synopsis Estimation of Stable Distributions by Indirect Inference by : René Garcia
Download or read book Estimation of Stable Distributions by Indirect Inference written by René Garcia and published by . This book was released on 2009 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article deals with the estimation of the parameters of an a-stable distribution with indirect inference, using the skewed-t distribution as an auxiliary model. The latter distribution appears as a good candidate since it has the same number of parameters as the a-stable distribution, with each parameter playing a similar role. To improve the properties of the estimator in finite sample, we use constrained indirect inference. In a Monte Carlo study we show that this method delivers estimators with good properties in finite sample. We provide an empirical application to the distribution of jumps in the Samp;P 500 index returns.
Book Synopsis Estimation of Stable Distributions by Indirect Inference by : René Garcia
Download or read book Estimation of Stable Distributions by Indirect Inference written by René Garcia and published by . This book was released on 2006 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parameter Estimation for Stable Distributions by : Gaoyuan Tian
Download or read book Parameter Estimation for Stable Distributions written by Gaoyuan Tian and published by . This book was released on 2016 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stable distributions are important family of parametric distributions widely used in signal processing as well as in mathematical finance. Estimation of the parameters of this model, is not quite straightforward due to the fact that there is no closed-form expression for their probability density function. Besides the computationally intensive maximum likelihood method where the density has to be evaluated numerically, there are some existing adhoc methods such as the quantile method, and a regression based method. These are introduced in Chapter 2. In this thesis, we introduce two new approaches: One, a spacing based estimation method introduced in Chapter 3 and two, an indirect inference method considered in Chapter 4. Simulation studies show that both these methods are very robust and efficient and do as well or better than the existing methods in most cases. Finally in Chapter 5, we use indirect inference approach to estimate the best fitting income distribution based on limited information that is often available.
Book Synopsis Estimating Stable Latent Factor Models by Indirect Inference by : Giorgio Calzolari
Download or read book Estimating Stable Latent Factor Models by Indirect Inference written by Giorgio Calzolari and published by . This book was released on 2016 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial returns exhibit common behavior described at best by factor models, but also fat tails, which may be captured by stable distributions. This paper concentrates on estimating factor models with multivariate stable distributed and independent latent factors and idiosyncratic noises under the assumption of time constant distribution (static factor models) or time-varying conditional distribution (GARCH factor models). While the simulation from such a distribution is straightforward, the estimation encounters difficulties. These difficulties are overcome in this paper by implementing the indirect inference estimation method with the multivariate Student's t as the auxiliary distribution.
Book Synopsis One-dimensional Stable Distributions by : V. M. Zolotarev
Download or read book One-dimensional Stable Distributions written by V. M. Zolotarev and published by American Mathematical Soc.. This book was released on 1986-06-30 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book specifically devoted to a systematic exposition of the essential facts known about the properties of stable distributions. In addition to its main focus on the analytic properties of stable laws, the book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding to these laws.
Book Synopsis Univariate Stable Distributions by : John P. Nolan
Download or read book Univariate Stable Distributions written by John P. Nolan and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.
Book Synopsis Estimation and Approximation of Tempered Stable Distribution by : Peipei Shi
Download or read book Estimation and Approximation of Tempered Stable Distribution written by Peipei Shi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Tempered stable random variables have a LePage like series representation, which was first introduced by Rosi¶nski. In this dissertation, we study the accuracy of the Rosi¶nski representation as determined by the convergence rates of the series. We also study estimators of parameters of certain tempered stable distributions and construct their confidence intervals. Finally, we present several simulation results for the Gamma-tempered random variable.
Book Synopsis Fundamental Statistical Inference by : Marc S. Paolella
Download or read book Fundamental Statistical Inference written by Marc S. Paolella and published by John Wiley & Sons. This book was released on 2018-06-19 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamental Statistical Inference by : Marc S. Paolella
Download or read book Fundamental Statistical Inference written by Marc S. Paolella and published by John Wiley & Sons. This book was released on 2018-09-04 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Parameters Estimation of the Discrete Stable Distribution by : Shu Mei Jiang
Download or read book Parameters Estimation of the Discrete Stable Distribution written by Shu Mei Jiang and published by . This book was released on 2006 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stable Distributions in Statistical Inference by : William Hermas DuMouchel
Download or read book Stable Distributions in Statistical Inference written by William Hermas DuMouchel and published by . This book was released on 1971 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stable distributions in statistical inference by : William H. DuMouchel
Download or read book Stable distributions in statistical inference written by William H. DuMouchel and published by . This book was released on 1978 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management by : Michele Leonardo Bianchi
Download or read book Handbook Of Heavy-tailed Distributions In Asset Management And Risk Management written by Michele Leonardo Bianchi and published by World Scientific. This book was released on 2019-03-08 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
Book Synopsis STATISTICAL INFERENCE FOR NON REGULAR FAMILY OF DISTRIBUTIONS (UNIFIED THEORY) by : Milind B. Bhatt
Download or read book STATISTICAL INFERENCE FOR NON REGULAR FAMILY OF DISTRIBUTIONS (UNIFIED THEORY) written by Milind B. Bhatt and published by Lulu.com. This book was released on with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Inference in Stable Distributions Based on Asymptotic Normality of the Sample Characteristic Function by : David Charles Kleinman
Download or read book Statistical Inference in Stable Distributions Based on Asymptotic Normality of the Sample Characteristic Function written by David Charles Kleinman and published by . This book was released on 1977 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Information Science, Engineering and Technology by : Gabriella Bognár
Download or read book Applied Information Science, Engineering and Technology written by Gabriella Bognár and published by Springer Science & Business Media. This book was released on 2013-09-30 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of the book is to give a selection from the papers, which summarize several important results obtained within the framework of the József Hatvany Doctoral School operating at the University of Miskolc, Hungary. In accordance with the three main research areas of the Doctoral School established for Information Science, Engineering and Technology, the papers can be classified into three groups. They are as follows: (1) Applied Computational Science; (2) Production Information Engineering (IT for Manufacturing included); (3) Material Stream Systems and IT for Logistics. As regards the first area, some papers deal with special issues of algorithms theory and its applications, with computing algorithms for engineering tasks, as well as certain issues of data base systems and knowledge intensive systems. Related to the second research area, the focus is on Production Information Engineering with special regard to discrete production processes. In the second research area the papers show some new integrated systems suitable for optimizing discrete production processes in a top-down way. The papers connecting with the third research field deal with different issues of materials stream systems and logistics, taking into consideration of applied mathematical models and IT-tools. The book makes an effort to ensure certain equilibrium between theory and practice and to show some new approach both from theoretical modelling aspect, as well as experimental and practical point of view.
Book Synopsis One-Dimensional Stable Distributions by : V. M. Zolotarev
Download or read book One-Dimensional Stable Distributions written by V. M. Zolotarev and published by . This book was released on 1986 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book specifically devoted to a systematic exposition of the essential facts known about the properties of stable distributions. In addition to its main focus on the analytic properties of stable laws, the book also includes examples of the occurrence of stable distributions in applied problems and a chapter on the problem of statistical estimation of the parameters determining stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding to these laws.
