Download or read book Bayesian Bandwidth Selection in Nonparametric Time varying Coefficient Models written by Tingting Cheng and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bayesian Bandwidth Estimation in Varying coefficient Time Series Models written by Tingting Cheng and published by . This book was released on 2014 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates three main topics, which are bandwidth selection for local linear estimation of time-varying coefficient time series models, nonparametric estimation of functional coefficient time series models with trending regressors and semiparametric localised bandwidth selection in kernel density estimation. First, we propose a Bayesian approach to bandwidth selection for local linear estimation of time-varying coefficient time series models, where the errors are assumed to follow the Gaussian kernel error density. A Markov chain Monte Carlo algorithm is presented to simultaneously estimate the bandwidths for local linear estimators in the regression function and the bandwidth for the Gaussian kernel error-density estimator. A Monte Carlo simulation study shows that: 1) our proposed Bayesian approach achieves better performance in estimating the bandwidths for local linear estimators than normal reference rule and cross-validation; and 2) compared with the parametric assumption of either the Gaussian or a mixture of two Gaussians, Gaussian kernel error-density assumption is a data-driven choice and helps gain robustness in terms of different specifications of the true error density. Moreover, we apply our proposed Bayesian sampling method to the estimation of bandwidth for the time-varying coefficient models that explain Okun's law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric forms of its time-varying coefficients. Second, we develop a functional coefficient time series model with trending regressors. We propose a local linear estimation method to estimate the unknown coefficient functions. The asymptotic distributions of the proposed local linear estimator are established under mild conditions. We further propose a Bayesian approach to select bandwidths involved in the proposed local linear estimator. Several numerical examples are provided to illustrate the finite sample behavior of the proposed methods. The results show that the local linear estimator works very well and the proposed Bayesian bandwidth selection method is better than cross-validation method. Furthermore, we employ the functional coefficient model to study the relationship between consumption per capita and income per capita in the U.S. and the results show that this functional coefficient model with our proposed local linear estimator and Bayesian bandwidth selection method performs better than other competing models in terms of both in-sample fitting and out-of-sample forecasting. Third, we propose a semiparametric localised bandwidth estimator for kernel density estimation based on strictly stationary mixing processes. We prove that the semiparametric localised bandwidth estimator is asymptotically normally distributed with root-n rate of convergence. To carry out the computation of the semiparametric localised bandwidth estimator for a given sample of data, we propose a sampling-based likelihood approach to hyperparameter estimation. Monte Carlo simulation studies show that the proposed hyperparameter estimation approach works very well, and that the proposed semiparametric localised bandwidth estimator outperforms its competitors. Applications of the new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate, as well as the S&P 500 daily return under conditional heteroscedasticity, demonstrate the effectiveness and competitiveness of the proposed semiparametric localised bandwidth. In addition, we present an easily computable expression for integrated squared error of normal density estimators, mixture of two normals density estimators and Gaussian kernel density estimators under different specifications of the true density. This provides a new way of evaluating the performance of the above three common-used density estimators. The numerical studies show that: 1) closed-form of integrated squared error is more accurate than grid-point approximation; 2) gird-point approximation is not robust, especially when the true density is asymmetric; 3) when the true density is neither normal nor mixture normal densities, Gaussian kernel density estimators can provide us with more accurate estimation.
Download or read book Nonparametric Regression and Generalized Linear Models written by P.J. Green and published by CRC Press. This book was released on 1993-05-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonparametric Regression and Generalized Linear Models focuses on the roughness penalty method of nonparametric smoothing and shows how this technique provides a unifying approach to a wide range of smoothing problems. The emphasis is methodological rather than theoretical, and the authors concentrate on statistical and computation issues. Real data examples are used to illustrate the various methods and to compare them with standard parametric approaches. The mathematical treatment is self-contained and depends mainly on simple linear algebra and calculus. This monograph will be useful both as a reference work for research and applied statisticians and as a text for graduate students.
Download or read book Nonparametric Kernel Density Estimation and Its Computational Aspects written by Artur Gramacki and published by Springer. This book was released on 2017-12-21 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.
Download or read book Nonlinear Time Series written by Jianqing Fan and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.
Download or read book Bayesian Bandwidth Selection for a Nonparametric Regression Model with Mixed Types of Regressors written by Xibin Zhang and published by . This book was released on 2013 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric Regression Methods for Longitudinal Data Analysis written by Hulin Wu and published by John Wiley & Sons. This book was released on 2006-05-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incorporates mixed-effects modeling techniques for more powerful and efficient methods This book presents current and effective nonparametric regression techniques for longitudinal data analysis and systematically investigates the incorporation of mixed-effects modeling techniques into various nonparametric regression models. The authors emphasize modeling ideas and inference methodologies, although some theoretical results for the justification of the proposed methods are presented. With its logical structure and organization, beginning with basic principles, the text develops the foundation needed to master advanced principles and applications. Following a brief overview, data examples from biomedical research studies are presented and point to the need for nonparametric regression analysis approaches. Next, the authors review mixed-effects models and nonparametric regression models, which are the two key building blocks of the proposed modeling techniques. The core section of the book consists of four chapters dedicated to the major nonparametric regression methods: local polynomial, regression spline, smoothing spline, and penalized spline. The next two chapters extend these modeling techniques to semiparametric and time varying coefficient models for longitudinal data analysis. The final chapter examines discrete longitudinal data modeling and analysis. Each chapter concludes with a summary that highlights key points and also provides bibliographic notes that point to additional sources for further study. Examples of data analysis from biomedical research are used to illustrate the methodologies contained throughout the book. Technical proofs are presented in separate appendices. With its focus on solving problems, this is an excellent textbook for upper-level undergraduate and graduate courses in longitudinal data analysis. It is also recommended as a reference for biostatisticians and other theoretical and applied research statisticians with an interest in longitudinal data analysis. Not only do readers gain an understanding of the principles of various nonparametric regression methods, but they also gain a practical understanding of how to use the methods to tackle real-world problems.
Download or read book Handbook of Bayesian Variable Selection written by Mahlet G. Tadesse and published by CRC Press. This book was released on 2021-12-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material
Download or read book Bayesian Nonparametric Data Analysis written by Peter Müller and published by Springer. This book was released on 2015-06-17 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews nonparametric Bayesian methods and models that have proven useful in the context of data analysis. Rather than providing an encyclopedic review of probability models, the book’s structure follows a data analysis perspective. As such, the chapters are organized by traditional data analysis problems. In selecting specific nonparametric models, simpler and more traditional models are favored over specialized ones. The discussed methods are illustrated with a wealth of examples, including applications ranging from stylized examples to case studies from recent literature. The book also includes an extensive discussion of computational methods and details on their implementation. R code for many examples is included in online software pages.
Download or read book Nonparametric and Semiparametric Methods in Econometrics and Statistics written by William A. Barnett and published by Cambridge University Press. This book was released on 1991-06-28 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers from a 1988 symposium on the estimation and testing of models that impose relatively weak restrictions on the stochastic behaviour of data.
Download or read book Nonparametric and Semiparametric Models written by Wolfgang Karl Härdle and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.
Download or read book The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics written by Jeffrey Racine and published by Oxford University Press. This book was released on 2014-04 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, edited by Jeffrey Racine, Liangjun Su, and Aman Ullah, contains the latest research on nonparametric and semiparametric econometrics and statistics. Chapters by leading international econometricians and statisticians highlight the interface between econometrics and statistical methods for nonparametric and semiparametric procedures.
Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.
Download or read book Kernel Smoothing written by M.P. Wand and published by CRC Press. This book was released on 1994-12-01 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets. The basic principle is that local averaging or smoothing is performed with respect to a kernel function. This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilita
Download or read book Recent Advances and Future Directions in Causality Prediction and Specification Analysis written by Xiaohong Chen and published by Springer Science & Business Media. This book was released on 2012-08-01 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles that present the most recent cutting edge results on specification and estimation of economic models written by a number of the world’s foremost leaders in the fields of theoretical and methodological econometrics. Recent advances in asymptotic approximation theory, including the use of higher order asymptotics for things like estimator bias correction, and the use of various expansion and other theoretical tools for the development of bootstrap techniques designed for implementation when carrying out inference are at the forefront of theoretical development in the field of econometrics. One important feature of these advances in the theory of econometrics is that they are being seamlessly and almost immediately incorporated into the “empirical toolbox” that applied practitioners use when actually constructing models using data, for the purposes of both prediction and policy analysis and the more theoretically targeted chapters in the book will discuss these developments. Turning now to empirical methodology, chapters on prediction methodology will focus on macroeconomic and financial applications, such as the construction of diffusion index models for forecasting with very large numbers of variables, and the construction of data samples that result in optimal predictive accuracy tests when comparing alternative prediction models. Chapters carefully outline how applied practitioners can correctly implement the latest theoretical refinements in model specification in order to “build” the best models using large-scale and traditional datasets, making the book of interest to a broad readership of economists from theoretical econometricians to applied economic practitioners.
Download or read book Bayesian Varying coefficient Models Using Adaptive Regression Splines written by Clemens Biller and published by . This book was released on 2000 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Machine Learning and Data Mining in Pattern Recognition written by Petra Perner and published by Springer. This book was released on 2017-07-01 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Machine Learning and Data Mining in Pattern Recognition, MLDM 2017, held in New York, NY, USA in July/August 2017.The 31 full papers presented in this book were carefully reviewed and selected from 150 submissions. The topics range from theoretical topics for classification, clustering, association rule and pattern mining to specific data mining methods for the different multi-media data types such as image mining, text mining, video mining, and Web mining.
