Download or read book Bayesian Empirical Likelihood for Quantile Regression written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Quantile Regression written by Tony Lancaster and published by . This book was released on 2006 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent work by Schennach(2005) has opened the way to a Bayesian treatment of quantile regression. Her method, called Bayesian exponentially tilted empirical likelihood (BETEL), provides a likelihood for data y subject only to a set of m moment conditions of the form Eg(y, amp;θ) = 0 where amp;θ is a k dimensional parameter of interest and k may be smaller, equal to or larger than m. The method may be thought of as construction of a likelihood supported on the n data points that is minimally informative, in the sense of maximum entropy, subject to the moment conditions. Specifically the probabilities {pi} attached to the n data points are chosen to solve.
Download or read book Bayesian Empirical Likelihood for Linear Regression and Penalized Regression written by Adel Bedoui and published by . This book was released on 2017 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The likelihood function plays an essential role in statistical analysis. It helps to estimate a set of parameters of interest. To make inferences, usually one must specify a parametric model given data, which is a challenging task because it requires specification of a correct distribution, and this parametric model may be prone to bias that arises either from the estimation of a parameter or an incorrect specification of the probability distribution. Non-parametric approaches are used as a remedy to overcome the misspecification of the model but can be computationally costly. In this dissertation, we proposed an alternative approach based on Bayesian empirical likelihood for linear regression and penalized regression. This method is semi-parametric because it combines a nonparametric and a parametric model. The advantage of this approach is that it does not require the assumption of a parametric model nor the linearity of estimators; that is, we avoided problems with model misspecification. By using a Hamiltonian Monte Carlo, we averted the problem of convergence and the daunting task of finding an adequate proposal density in the Metropolis-Hastings method. Additionally, we showed that the maximum empirical likelihood estimator is consistent. Moreover, the resulting posterior density under the Bayesian empirical likelihood framework lacks a closed form, which makes it difficult to obtain the exact distribution. For this purpose, we derived the asymptotic distribution of the regression parameters in the linear regression along with Bayesian credible intervals.
Download or read book Smoothed Empirical Likelihood Methods for Quantile Regression Models written by Yoon-Jae Whang and published by . This book was released on 2004 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Quantile Regression written by Roger Koenker and published by CRC Press. This book was released on 2017-10-12 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression constitutes an ensemble of statistical techniques intended to estimate and draw inferences about conditional quantile functions. Median regression, as introduced in the 18th century by Boscovich and Laplace, is a special case. In contrast to conventional mean regression that minimizes sums of squared residuals, median regression minimizes sums of absolute residuals; quantile regression simply replaces symmetric absolute loss by asymmetric linear loss. Since its introduction in the 1970's by Koenker and Bassett, quantile regression has been gradually extended to a wide variety of data analytic settings including time series, survival analysis, and longitudinal data. By focusing attention on local slices of the conditional distribution of response variables it is capable of providing a more complete, more nuanced view of heterogeneous covariate effects. Applications of quantile regression can now be found throughout the sciences, including astrophysics, chemistry, ecology, economics, finance, genomics, medicine, and meteorology. Software for quantile regression is now widely available in all the major statistical computing environments. The objective of this volume is to provide a comprehensive review of recent developments of quantile regression methodology illustrating its applicability in a wide range of scientific settings. The intended audience of the volume is researchers and graduate students across a diverse set of disciplines.
Download or read book Empirical Bayes and Likelihood Inference written by S.E. Ahmed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian and such approaches to inference have a number of points of close contact, especially from an asymptotic point of view. Both emphasize the construction of interval estimates of unknown parameters. In this volume, researchers present recent work on several aspects of Bayesian, likelihood and empirical Bayes methods, presented at a workshop held in Montreal, Canada. The goal of the workshop was to explore the linkages among the methods, and to suggest new directions for research in the theory of inference.
Download or read book Empirical Likelihood Methods in Biomedicine and Health written by Albert Vexler and published by CRC Press. This book was released on 2018-09-03 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Likelihood Methods in Biomedicine and Health provides a compendium of nonparametric likelihood statistical techniques in the perspective of health research applications. It includes detailed descriptions of the theoretical underpinnings of recently developed empirical likelihood-based methods. The emphasis throughout is on the application of the methods to the health sciences, with worked examples using real data. Provides a systematic overview of novel empirical likelihood techniques. Presents a good balance of theory, methods, and applications. Features detailed worked examples to illustrate the application of the methods. Includes R code for implementation. The book material is attractive and easily understandable to scientists who are new to the research area and may attract statisticians interested in learning more about advanced nonparametric topics including various modern empirical likelihood methods. The book can be used by graduate students majoring in biostatistics, or in a related field, particularly for those who are interested in nonparametric methods with direct applications in Biomedicine.
Download or read book Topics on Methodological and Applied Statistical Inference written by Tonio Di Battista and published by Springer. This book was released on 2016-10-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together selected peer-reviewed contributions from various research fields in statistics, and highlights the diverse approaches and analyses related to real-life phenomena. Major topics covered in this volume include, but are not limited to, bayesian inference, likelihood approach, pseudo-likelihoods, regression, time series, and data analysis as well as applications in the life and social sciences. The software packages used in the papers are made available by the authors. This book is a result of the 47th Scientific Meeting of the Italian Statistical Society, held at the University of Cagliari, Italy, in 2014.
Download or read book Bayesian Inference in the Social Sciences written by Ivan Jeliazkov and published by John Wiley & Sons. This book was released on 2014-11-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents new models, methods, and techniques and considers important real-world applications in political science, sociology, economics, marketing, and finance Emphasizing interdisciplinary coverage, Bayesian Inference in the Social Sciences builds upon the recent growth in Bayesian methodology and examines an array of topics in model formulation, estimation, and applications. The book presents recent and trending developments in a diverse, yet closely integrated, set of research topics within the social sciences and facilitates the transmission of new ideas and methodology across disciplines while maintaining manageability, coherence, and a clear focus. Bayesian Inference in the Social Sciences features innovative methodology and novel applications in addition to new theoretical developments and modeling approaches, including the formulation and analysis of models with partial observability, sample selection, and incomplete data. Additional areas of inquiry include a Bayesian derivation of empirical likelihood and method of moment estimators, and the analysis of treatment effect models with endogeneity. The book emphasizes practical implementation, reviews and extends estimation algorithms, and examines innovative applications in a multitude of fields. Time series techniques and algorithms are discussed for stochastic volatility, dynamic factor, and time-varying parameter models. Additional features include: Real-world applications and case studies that highlight asset pricing under fat-tailed distributions, price indifference modeling and market segmentation, analysis of dynamic networks, ethnic minorities and civil war, school choice effects, and business cycles and macroeconomic performance State-of-the-art computational tools and Markov chain Monte Carlo algorithms with related materials available via the book’s supplemental website Interdisciplinary coverage from well-known international scholars and practitioners Bayesian Inference in the Social Sciences is an ideal reference for researchers in economics, political science, sociology, and business as well as an excellent resource for academic, government, and regulation agencies. The book is also useful for graduate-level courses in applied econometrics, statistics, mathematical modeling and simulation, numerical methods, computational analysis, and the social sciences.
Download or read book Bayesian Quantile Regression Using Flexible Likelihood Functions written by Aziz Awadhallah S. Aljuaid and published by . This book was released on 2017 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Empirical Likelihood written by Art B. Owen and published by CRC Press. This book was released on 2001-05-18 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al
Download or read book Bayesian Quantile Linear Regression written by Yang Feng and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantile regression, as a supplement to the mean regression, is often used when a comprehensive relationship between the response variable and the explanatory variables is desired. The traditional frequentists0́9 approach to quantile regression was well developed with asymptotic theories and efficient algorithms. However not much work has been done under the Bayesian framework. The most challenging problem for Bayesian quantile regression is that the likelihood is usually not available unless a certain distribution for the error is assumed. In this dissertation, we propose two Bayesian quantile regression methods: the data generating process based method (DG) and the linearly interpolated density based method (LID). Markov chain Monte Carlo algorithms are developed to implement the proposed methods. We provide the convergence property of the algorithms and numerically verify the theoretical results. We compare the proposed methods with some existing methods through simulation studies, and apply our method to the birth weight data. Unlike most of the existing methods which aim at tackling one quantile at a time, our proposed methods aim at estimating the joint posterior distribution of multiple quantiles and achieving global efficiency for all quantiles of interest and functions of those quantiles. From the simulation results, we found that LID could produce more efficient estimates than some existing methods. In particular, for estimating the difference of quantiles, LID has a big advantage over other existing methods.
Download or read book Asymptotic Statistics written by Petr Mandl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: In particular up-to-date-information is presented in detection of systematic changes, in series of observation, in robust regression analysis, in numerical empirical processes and in related areas of actuarial sciences.
Download or read book Likelihood and Bayesian Inference written by Leonhard Held and published by Springer Nature. This book was released on 2020-03-31 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.
Download or read book Bayesian Analysis in Statistics and Econometrics written by Donald A. Berry and published by John Wiley & Sons. This book was released on 1996 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a definitive work that captures the current state of knowledge of Bayesian Analysis in Statistics and Econometrics and attempts to move it forward. It covers such topics as foundations, forecasting inferential matters, regression, computation and applications.
Download or read book Empirical Likelihood Method in Survival Analysis written by Mai Zhou and published by CRC Press. This book was released on 2015-06-17 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Likelihood Method in Survival Analysis explains how to use the empirical likelihood method for right censored survival data. The author uses R for calculating empirical likelihood and includes many worked out examples with the associated R code. The datasets and code are available for download on his website and CRAN. The book focuses on all the standard survival analysis topics treated with empirical likelihood, including hazard functions, cumulative distribution functions, analysis of the Cox model, and computation of empirical likelihood for censored data. It also covers semi-parametric accelerated failure time models, the optimality of confidence regions derived from empirical likelihood or plug-in empirical likelihood ratio tests, and several empirical likelihood confidence band results. While survival analysis is a classic area of statistical study, the empirical likelihood methodology has only recently been developed. Until now, just one book was available on empirical likelihood and most statistical software did not include empirical likelihood procedures. Addressing this shortfall, this book provides the functions to calculate the empirical likelihood ratio in survival analysis as well as functions related to the empirical likelihood analysis of the Cox regression model and other hazard regression models.
Download or read book Markov Chain Monte Carlo Approach to Classical Estimation written by Victor Chernozhukov and published by . This book was released on 2002 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies computationally and theoretically attractive estimators referred here as to the Laplace type estimators (LTE). The LTE include means and quantiles of Quasi-posterior distributions defined as transformations of general(non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile regression, nonlinear IV, GMM, and value-at-risk, models. The LTE's are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained and illustrated for regular cases. Keywords: Laplace, Bayes, Markov Chain Monte Carlo, GMM, Instrumental Regression, Censored Quantile Regression, Instrumental Quantile Regression, Empirical Likelihood, Value-at-Risk. JEL Classification: C10, C11, C13, C15.
