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Author: Monica Billio Publisher: ISBN: Category : Languages : en Pages :
Book Description
The class of parametric dynamic latent variable models is becoming increasingly popular in finance and economics. Latent factor models, switching regimes models, stochastic volatility models, and dynamic disequilibrium models are only a few examples of this class of model. Inference in this class may be difficult since the computation of the likelihood function requires integrating out the unobservable components and calculating very high dimensional integrals. We propose an estimation procedure that could be applied to any dynamic latent model. The approach is based on the indirect inference principle and, in order to capture the dynamic features of these models, the binding functions are conditional expectations of functions of the endogenous variables given their past values. These conditional expectations are estimated by a nonparametric kernel-based approach. Unlike the indirect inference method, no optimization step is involved in the computation of the binding function and the approach is useful when no convenient auxiliary model is available. In spite of the nonparametric feature of the approach, the estimator is consistent and its convergence rate may be arbitrarily close to the classical parametric one. Moreover, a scoring method to select the best binding functions is proposed. Finally, some Monte Carlo experiments for factor ARCH and GARCH models show the feasibility of the approach.
Author: Monica Billio Publisher: ISBN: Category : Languages : en Pages :
Book Description
The class of parametric dynamic latent variable models is becoming increasingly popular in finance and economics. Latent factor models, switching regimes models, stochastic volatility models, and dynamic disequilibrium models are only a few examples of this class of model. Inference in this class may be difficult since the computation of the likelihood function requires integrating out the unobservable components and calculating very high dimensional integrals. We propose an estimation procedure that could be applied to any dynamic latent model. The approach is based on the indirect inference principle and, in order to capture the dynamic features of these models, the binding functions are conditional expectations of functions of the endogenous variables given their past values. These conditional expectations are estimated by a nonparametric kernel-based approach. Unlike the indirect inference method, no optimization step is involved in the computation of the binding function and the approach is useful when no convenient auxiliary model is available. In spite of the nonparametric feature of the approach, the estimator is consistent and its convergence rate may be arbitrarily close to the classical parametric one. Moreover, a scoring method to select the best binding functions is proposed. Finally, some Monte Carlo experiments for factor ARCH and GARCH models show the feasibility of the approach.
Author: Alain Monfort Publisher: ISBN: Category : Languages : en Pages :
Book Description
The class of parametric dynamic latent variable models is becoming increasingly popular in finance and economics. Latent factor models, switching regimes models, stochastic volatility models, and dynamic disequilibrium models are only a few examples of this class of model. Inference in this class may be difficult since the computation of the likelihood function requires integrating out the unobservable components and calculating very high dimensional integrals. We propose an estimation procedure that could be applied to any dynamic latent model. The approach is based on the indirect inference principle and, in order to capture the dynamic features of these models, the binding functions are conditional expectations of functions of the endogenous variables given their past values. These conditional expectations are estimated by a nonparametric kernel-based approach. Unlike the indirect inference method, no optimization step is involved in the computation of the binding function and the approach is useful when no convenient auxiliary model is available. In spite of the nonparametric feature of the approach, the estimator is consistent and its convergence rate may be arbitrarily close to the classical parametric one. Moreover, a scoring method to select the best binding functions is proposed. Finally, some Monte Carlo experiments for factor ARCH and GARCH models show the feasibility of the approach.
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: David Frazier Publisher: ISBN: Category : Languages : en Pages : 50
Book Description
Indirect inference requires simulating realisations of endogenous variables from the model under study. When the endogenous variables are discontinuous functions of the model parameters, the resulting indirect inference criterion function is discontinuous and does not permit the use of derivative-based optimisation routines. Using a change of variables technique, we propose a novel simulation algorithm that alleviates the discontinuities inherent in such indirect inference criterion functions, and permits the application of derivative-based optimisation routines to estimate the unknown model parameters. Unlike competing approaches, this approach does not rely on kernel smoothing or bandwidth parameters. Several Monte Carlo examples that have featured in the literature on indirect inference with discontinuous outcomes illustrate the approach, and demonstrate the superior performance of this approach over existing alternatives.
Author: Roberto Mariano Publisher: Cambridge University Press ISBN: 9780521591126 Category : Business & Economics Languages : en Pages : 488
Book Description
This substantial volume has two principal objectives. First it provides an overview of the statistical foundations of Simulation-based inference. This includes the summary and synthesis of the many concepts and results extant in the theoretical literature, the different classes of problems and estimators, the asymptotic properties of these estimators, as well as descriptions of the different simulators in use. Second, the volume provides empirical and operational examples of SBI methods. Often what is missing, even in existing applied papers, are operational issues. Which simulator works best for which problem and why? This volume will explicitly address the important numerical and computational issues in SBI which are not covered comprehensively in the existing literature. Examples of such issues are: comparisons with existing tractable methods, number of replications needed for robust results, choice of instruments, simulation noise and bias as well as efficiency loss in practice.
Author: Luis Alonso-Ovalle Publisher: OUP Oxford ISBN: 0191643106 Category : Language Arts & Disciplines Languages : en Pages : 322
Book Description
This book brings together novel work on the semantics and pragmatics of certain indefinite expressions that also convey modality. These epistemic indefinites are determiners or pronouns that signal ignorance on the part of the speaker, such as German irgendein and Spanish algún: the sentence María se casó con algún medico ('Maria married some doctor or other') both makes an existential statement that there is a doctor that Maria married and signals the speaker's inability or unwillingness to identify the doctor in question. Although epistemic indefinites have featured in recent semantic literature, a full understanding of the phenomenon is still lacking: there is currently no agreement on the source of their epistemic component; there is insufficient cross-linguistic data to develop a semantic typology of these items; and the parallelisms and differences between epistemic indefinites and other expressions that convey epistemic modality have not been explored in depth. In this volume, a team of experts in the field offer novel empirical observations and important theoretical insights on epistemic indefinites and related topics such as modal free relatives, modified numerals, and epistemic modals. They provide a coherent overview of the issues that shape the subject as well as placing them in the context of current semantic research, moving towards the development of a semantic typology of epistemic indefinites that explores the place of these expressions within a general typology of modal items.
Author: Rizky Reza Fauzi Publisher: ISBN: 9789819918638 Category : Languages : en Pages : 0
Book Description
This book presents a study of statistical inferences based on the kernel-type estimators of distribution functions. The inferences involve matters such as quantile estimation, nonparametric tests, and mean residual life expectation, to name just some. Convergence rates for the kernel estimators of density functions are slower than ordinary parametric estimators, which have root-n consistency. If the appropriate kernel function is used, the kernel estimators of the distribution functions recover the root-n consistency, and the inferences based on kernel distribution estimators have root-n consistency. Further, the kernel-type estimator produces smooth estimation results. The estimators based on the empirical distribution function have discrete distribution, and the normal approximation cannot be improved-that is, the validity of the Edgeworth expansion cannot be proved. If the support of the population density function is bounded, there is a boundary problem, namely the estimator does not have consistency near the boundary. The book also contains a study of the mean squared errors of the estimators and the Edgeworth expansion for quantile estimators.
Author: Masashi Sugiyama Publisher: Cambridge University Press ISBN: 0521190177 Category : Computers Languages : en Pages : 343
Book Description
This book introduces theories, methods and applications of density ratio estimation, a newly emerging paradigm in the machine learning community.
Author: Marc S. Paolella Publisher: John Wiley & Sons ISBN: 1119417880 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: Publisher: Morgan Kaufmann ISBN: 0080963544 Category : Mathematics Languages : en Pages : 667
Book Description
Handbook of Statistics_29B contains the most comprehensive account of sample surveys theory and practice to date. It is a second volume on sample surveys, with the goal of updating and extending the sampling volume published as volume 6 of the Handbook of Statistics in 1988. The present handbook is divided into two volumes (29A and 29B), with a total of 41 chapters, covering current developments in almost every aspect of sample surveys, with references to important contributions and available software. It can serve as a self contained guide to researchers and practitioners, with appropriate balance between theory and real life applications. Each of the two volumes is divided into three parts, with each part preceded by an introduction, summarizing the main developments in the areas covered in that part. Volume 1 deals with methods of sample selection and data processing, with the later including editing and imputation, handling of outliers and measurement errors, and methods of disclosure control. The volume contains also a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses. Volume 2 is concerned with inference, distinguishing between design-based and model-based methods and focusing on specific problems such as small area estimation, analysis of longitudinal data, categorical data analysis and inference on distribution functions. The volume contains also chapters dealing with case-control studies, asymptotic properties of estimators and decision theoretic aspects. Comprehensive account of recent developments in sample survey theory and practice Covers a wide variety of diverse applications Comprehensive bibliography
Author: Monica Billio
Author: Monica Billio
Author: Alain Monfort
Author: Marc S. Paolella
Author: David Frazier
Author: Roberto Mariano
Author: Luis Alonso-Ovalle
Author: Rizky Reza Fauzi
Author: Masashi Sugiyama
Author: Marc S. Paolella
Author: