Download or read book Asymptotics for LS GLS and Feasible GLS Statistics in an AR 1 Model with Conditional Heteroskedaticity written by Donald W. K. Andrews and published by . This book was released on 2008 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rho_n satisfies (i) n(1 - rho_n) -gt; infinity and (ii) n(1 - rho_n) -gt; h_1 lt; infinity as n -gt; infinity, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.

Download or read book Unit Root Tests in Time Series Volume 2 written by K. Patterson and published by Springer. This book was released on 2012-07-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Testing for a Unit Root is now an essential part of time series analysis but the literature on the topic is so large that knowing where to start is difficult even for the specialist. This book provides a way into the techniques of unit root testing, explaining the pitfalls and nonstandard cases, using practical examples and simulation analysis.

Download or read book Weighted Empiricals and Linear Models written by Hira L. Koul and published by IMS. This book was released on 1992 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book GLS Detrending and the Power of Unit Root and Stationarity Tests written by Jaeyoun Hwang and published by . This book was released on 1993 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Linear Mixed Models written by Walter W. Stroup and published by CRC Press. This book was released on 2024-05-21 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Linear Mixed Models: Modern Concepts, Methods, and Applications (2nd edition) presents an updated introduction to linear modeling using the generalized linear mixed model (GLMM) as the overarching conceptual framework. For students new to statistical modeling, this book helps them see the big picture – linear modeling as broadly understood and its intimate connection with statistical design and mathematical statistics. For readers experienced in statistical practice, but new to GLMMs, the book provides a comprehensive introduction to GLMM methodology and its underlying theory. Unlike textbooks that focus on classical linear models or generalized linear models or mixed models, this book covers all of the above as members of a unified GLMM family of linear models. In addition to essential theory and methodology, this book features a rich collection of examples using SAS® software to illustrate GLMM practice. This second edition is updated to reflect lessons learned and experience gained regarding best practices and modeling choices faced by GLMM practitioners. New to this edition are two chapters focusing on Bayesian methods for GLMMs. Key Features: • Most statistical modeling books cover classical linear models or advanced generalized and mixed models; this book covers all members of the GLMM family – classical and advanced models. • Incorporates lessons learned from experience and on-going research to provide up-to-date examples of best practices. • Illustrates connections between statistical design and modeling: guidelines for translating study design into appropriate model and in-depth illustrations of how to implement these guidelines; use of GLMM methods to improve planning and design. • Discusses the difference between marginal and conditional models, differences in the inference space they are intended to address and when each type of model is appropriate. • In addition to likelihood-based frequentist estimation and inference, provides a brief introduction to Bayesian methods for GLMMs. Walt Stroup is an Emeritus Professor of Statistics. He served on the University of Nebraska statistics faculty for over 40 years, specializing in statistical modeling and statistical design. He is a Fellow of the American Statistical Association, winner of the University of Nebraska Outstanding Teaching and Innovative Curriculum Award and author or co-author of three books on mixed models and their extensions. Marina Ptukhina (Pa-too-he-nuh), PhD, is an Associate Professor of Statistics at Whitman College. She is interested in statistical modeling, design and analysis of research studies and their applications. Her research includes applications of statistics to economics, biostatistics and statistical education. Ptukhina earned a PhD in Statistics from the University of Nebraska-Lincoln, a Master of Science degree in Mathematics from Texas Tech University and a Specialist degree in Management from The National Technical University "Kharkiv Polytechnic Institute." Julie Garai, PhD, is a Data Scientist at Loop. She earned her PhD in Statistics from the University of Nebraska-Lincoln and a bachelor’s degree in Mathematics and Spanish from Doane College. Dr Garai actively collaborates with statisticians, psychologists, ecologists, forest scientists, software engineers, and business leaders in academia and industry. In her spare time, she enjoys leisurely walks with her dogs, dance parties with her children, and playing the trombone.

Download or read book Weighted Empiricals and Linear Models written by Hira L. Koul and published by . This book was released on 2008* with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.

Download or read book Prior Information in Linear Models written by Helge Toutenburg and published by John Wiley & Sons. This book was released on 1982 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Likelihood Estimation of the Autoregressive Coefficients and Moving Average Covariances of Vector Autoregressive Moving Average Models written by Fereydoon Ahrabi and published by . This book was released on 1979 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to derive asymptotically efficient estimates for the autoregressive matrix coefficients and moving average covariance matrices of the vector autoregressive moving average (VARMA) models in both time and frequency domains. To do this we shall apply the Newton-Raphson and scoring methods to the maximum likelihood equations derived from modified likelihood functions under the Gaussian Assumption.

Download or read book Parameter Estimation and Hypothesis Testing in Linear Models written by Karl-Rudolf Koch and published by Springer. This book was released on 1988 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on theoretical geodesy deals with the estimation of unknown parameters, the testing of hypothesis and the estimation of intervals in linear models. The reader will find presentations of the Gauss-Markoff model, the analysis of variance, the multivariate model, the model with unknown variance and covariance components and the regression model, as well as the mixed model for estimation random parameters. To make the book self-contained most of the necessary theorems of vector and matrix-algebra and the probability distributions for the test statistics are derived. Students of geodesy, as well as of mathematics and engineering, will find the geodetical application of mathematical and statistical models extremely useful.

Download or read book A Refined Efficiency Rate for Ordinary Least Squares and Generalized Least Squares Estimators for a Linear Trend with Autoregressive Errors written by Jaechoul Lee and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: When a straight line is fitted to time series data, generalized least squares (GLS) estimators of the trend slope and intercept are attractive as they are unbiased and of minimum variance. However, computing GLS estimators is laborious as their form depends on the autocovariances of the regression errors. On the other hand, ordinary least squares (OLS) estimators are easy to compute and do not involve the error autocovariance structure. It has been known for 50 years that OLS and GLS estimators have the same asymptotic variance when the errors are second-order stationary. Hence, little precision is gained by using GLS estimators in stationary error settings. This article revisits this classical issue, deriving explicit expressions for the GLS estimators and their variances when the regression errors are drawn from an autoregressive process. These expressions are used to show that OLS methods are even more efficient than previously thought. Specifically, we show that the convergence rate of variance differences is one polynomial degree higher than that of least squares estimator variances. We also refine Grenander's (1954) variance ratio. An example is presented where our new rates cannot be improved upon. Simulations show that the results change little when the autoregressive parameters are estimated.

Download or read book An Iterative GLS Approach to Maximum Likelihood Estimation of Regression Models with Arima Errors written by Mark C. Otto and published by . This book was released on 1987 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We present a method for estimating regression models with autoregressive integrated moving average (ARIMA) time series errors. The method maximizes the likelihood for different groups of parameters (AR, regression, and MA) separately within each iteration. The idea is to gain numerical efficiency by using generalized least squares (GLS) to maximize the likelihood over the regression and the autoregressive parameters, leaving only the moving average parameter estimates to be obtained by a nonlinear optimization routine. The method uses the "exact likelihood" suggested by Hillmer and Tiao (1979) that is the exact likelihood for pure moving average models. Implementing the method amounts to feeding vectors of the regression and lagged dependent variable to routines that calculate exact likelihood residuals for pure MA models, and then doing regression with these residuals to get the regression and AR parameters. In this way the same software used for exact MA likelihood estimation may be easily modified and used to estimate models with AR and regression effects."

Download or read book GLS Estimation and Empirical Bayes Prediction for Linear Mixed Models with Heteroskedasticity and Sampling Weights written by Roy van der Weide and published by . This book was released on 2017 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: This note adapts results by Huang and Hidiroglou (2003) on Generalized Least Squares estimation and Empirical Bayes prediction for linear mixed models with sampling weights. The objective is to incorporate these results into the poverty mapping approach put forward by Elbers et al. (2003). The estimators presented here have been implemented in version 2.5 of POVMAP, the custom-made poverty mapping software developed by the World Bank.

Download or read book Asymptotic Behaviour of Weighted Least Squares Estimator in Linear Functional Error in variables Models written by Carleton University. Laboratory for Research in Statistics and Probability and published by . This book was released on 2001 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Maximum Likelihood Estimation of Parameters of an Autoregressive Process with Moving Average Residuals and Other Covariance Matrices with Linear Structure written by STANFORD UNIV CALIF DEPT OF STATISTICS. and published by . This book was released on 1973 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Linear Models written by Peter McCullagh and published by . This book was released on 1985 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book GLS Under Monotone Heteroskedasticity written by Yoichi Arai and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Density of the Sufficient Statistics for a Gaussian AR 1 Model in Terms of Generalized Functions written by G. Forchini and published by . This book was released on 2000 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: