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Estimating Weights In Heteroscedastic Regression Models By Applying Least Squares To Squared Or Absolute Residuals
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Book Synopsis Estimating Weights in Heteroscedastic Regression Models by Applying Least Squares to Squared Or Absolute Residuals by : Raymond J. Carroll
Download or read book Estimating Weights in Heteroscedastic Regression Models by Applying Least Squares to Squared Or Absolute Residuals written by Raymond J. Carroll and published by . This book was released on 1985 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document considers a nonlinear regression model for which the variances depend on a parametric function of known variables. The authors focus on estimating the variance function, after what it is typical to estimate the mean function by weighted least squares. Most often, squared residuals from an unweighted least squares fit are compared to their expectations and used to estimate the variance function. If properly weighted such methods are asymptotically equivalent to normal-theory maximum likelihood. Instead, one could use the deviations of the absolute residuals from their expectations. Constructed is such an estimator of the variance function based on absolute residuals whose asymptotic efficiency relative to maximum likelihood is precisely the same for symmetric errors as the asymptotic efficiency in the one-sample problem of the mean absolute deviation relative to the sample variance. The estimators are computable using nonlinear least squares software. The results hold with minimal distributional assumptions. (Author).
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1986 with total page 1362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applied Linear Statistical Models by : Michael H. Kutner
Download or read book Applied Linear Statistical Models written by Michael H. Kutner and published by McGraw-Hill/Irwin. This book was released on 2005 with total page 1396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear regression with one predictor variable; Inferences in regression and correlation analysis; Diagnosticis and remedial measures; Simultaneous inferences and other topics in regression analysis; Matrix approach to simple linear regression analysis; Multiple linear regression; Nonlinear regression; Design and analysis of single-factor studies; Multi-factor studies; Specialized study designs.
Book Synopsis Heteroscedastic Linear Model Estimation Based on Ranks by : Themba Louis Nyirenda
Download or read book Heteroscedastic Linear Model Estimation Based on Ranks written by Themba Louis Nyirenda and published by . This book was released on 2009 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: For standard estimators, data that are heteroscedastic in nature contain outlying values which can lead to poor performance. In this study, we present a robust interactive method for estimating the location and scale parameters in the general linear model, using a rank based method. It is assumed that the errors are symmetric about 0 and the variance function model is nonlinear with respect to the scale coefficients and the design. The function is known up to a scale constant. We propose taking the logarithm of the absolute values of the variance function to linearize it. The rank estimation of the scale coefficients amounts to regressing logs of absolute residuals from an initial rank based fit on to the design. The resulting scale coefficient estimates are used to form scale constants in a weighted signed-rank method. Thus, iterating between these two rank based methods leads to the desired estimates that are obtained from linear model fits for both types of coefficients. For the heteroscedastic linear model under consideration, this study has made the following contributions: (1) the asymptotic normality results that are established here show that the estimators are both consistent and highly efficient; (2) in each estimation problem, the Iterated Reweighted Least Squares (IRWLS) formulation for rank methods of Sievers and Abebe (2004) is employed with the other parameter substituted by their corresponding estimates from an appropriate iteration; (3) the high efficiency and good robustness qualities of the proposed method are confirmed by simulation trials that were conducted in two-sample problem, several groups and general linear models; (4) the inlier issue that is a consequence of employing the log transformation is also investigated and shown to be well curtailed by the proposed method and (5) finally, the method is shown to outperform other methods when applied to real life data from a Psychiatric Clinical Trial containing two treatments, one covariate, and one confounding variable. Thus, for samples larger than 20, the proposed method is highly robust and efficient under non-normal distributions.
Book Synopsis Government Reports Announcements & Index by :
Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1988-05 with total page 1298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quasi-Least Squares Regression by : Justine Shults
Download or read book Quasi-Least Squares Regression written by Justine Shults and published by CRC Press. This book was released on 2014-01-28 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on the authors’ substantial expertise in modeling longitudinal and clustered data, Quasi-Least Squares Regression provides a thorough treatment of quasi-least squares (QLS) regression—a computational approach for the estimation of correlation parameters within the framework of generalized estimating equations (GEEs). The authors present a detailed evaluation of QLS methodology, demonstrating the advantages of QLS in comparison with alternative methods. They describe how QLS can be used to extend the application of the traditional GEE approach to the analysis of unequally spaced longitudinal data, familial data, and data with multiple sources of correlation. In some settings, QLS also allows for improved analysis with an unstructured correlation matrix. Special focus is given to goodness-of-fit analysis as well as new strategies for selecting the appropriate working correlation structure for QLS and GEE. A chapter on longitudinal binary data tackles recent issues raised in the statistical literature regarding the appropriateness of semi-parametric methods, such as GEE and QLS, for the analysis of binary data; this chapter includes a comparison with the first-order Markov maximum-likelihood (MARK1ML) approach for binary data. Examples throughout the book demonstrate each topic of discussion. In particular, a fully worked out example leads readers from model building and interpretation to the planning stages for a future study (including sample size calculations). The code provided enables readers to replicate many of the examples in Stata, often with corresponding R, SAS, or MATLAB® code offered in the text or on the book’s website.
Book Synopsis Monthly Checklist of State Publications by : Library of Congress. Exchange and Gift Division
Download or read book Monthly Checklist of State Publications written by Library of Congress. Exchange and Gift Division and published by . This book was released on 1986 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual index to the monographs appears early in the following year.
Book Synopsis Seemingly Unrelated Regression Equations Models by : Virendera K. Srivastava
Download or read book Seemingly Unrelated Regression Equations Models written by Virendera K. Srivastava and published by CRC Press. This book was released on 1987-05-29 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seemingly unrelated regression equations model; The least squares estimator and its variants; Approximate destribution theory for feasible generalized least squares estimators; Exact finite-sample properties of feasible generalized least squares estimators; Iterative estimators; Shrinkage estimators; Autoregressive disturbances; Heteroscedastic disturbances; Constrained error covariance structures; Prior information; Some miscellaneous topics.
Book Synopsis Heteroskedasticity in Regression by : Robert L. Kaufman
Download or read book Heteroskedasticity in Regression written by Robert L. Kaufman and published by SAGE Publications. This book was released on 2013-06-28 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heteroskedasticity in Regression: Detection and Correction, by Robert Kaufman, covers the commonly ignored topic of heteroskedasticity (unequal error variances) in regression analyses and provides a practical guide for how to proceed in terms of testing and correction. Emphasizing how to apply diagnostic tests and corrections for heteroskedasticity in actual data analyses, the monograph offers three approaches for dealing with heteroskedasticity: (1) variance-stabilizing transformations of the dependent variable; (2) calculating robust standard errors, or heteroskedasticity-consistent standard errors; and (3) generalized least squares estimation coefficients and standard errors. The detection and correction of heteroskedasticity is illustrated with three examples that vary in terms of sample size and the types of units analyzed (individuals, households, U.S. states). Intended as a supplementary text for graduate-level courses and a primer for quantitative researchers, the book fills the gap between the limited coverage of heteroskedasticity provided in applied regression textbooks and the more theoretical statistical treatment in advanced econometrics textbooks.
Book Synopsis Transformation and Weighting in Regression by : Raymond J. Carroll
Download or read book Transformation and Weighting in Regression written by Raymond J. Carroll and published by Routledge. This book was released on 2017-10-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a careful review of the major statistical techniques used to analyze regression data with nonconstant variability and skewness. The authors have developed statistical techniques--such as formal fitting methods and less formal graphical techniques-- that can be applied to many problems across a range of disciplines, including pharmacokinetics, econometrics, biochemical assays, and fisheries research. While the main focus of the book in on data transformation and weighting, it also draws upon ideas from diverse fields such as influence diagnostics, robustness, bootstrapping, nonparametric data smoothing, quasi-likelihood methods, errors-in-variables, and random coefficients. The authors discuss the computation of estimates and give numerous examples using real data. The book also includes an extensive treatment of estimating variance functions in regression.
Book Synopsis Recent Accomplishments in Applied Forest Economics Research by : F. Helles
Download or read book Recent Accomplishments in Applied Forest Economics Research written by F. Helles and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this book were 'in a preliminary version' presented at an international con ference May 21-25, 2002 in Gilleleje, Denmark. It was a joint event, namely the biennial meeting of the Scandinavian Society of Forest Economics and the 3rd Berkeley-KVL Con ference. The Scandinavian Society of Forest Economics (SSFE) was established in 1958 as a forum for forest economists in the Nordic countries to meet and exchange ideas on research and education. Alternating between Denmark, Finland, Norway and Sweden, biennial ordinary meetings have taken place ever since. The number of participants has increased from 10-15 in the first decade to more than 80 in 2002. In the last two decades prominent researchers from outside Scandinavia have been invited to present papers at the biennial meetings and also to participate in ad hoc working groups. The Berkeley-KVL part of the conference is based on a research collaboration between The Royal Veterinary and Agricultural University (KVL), Copenhagen, University of Cali fornia at Berkeley, and Oregon State University. It was initiated in 1993 within the frame work of a research programme at KVL: 'Stochastic Decision Analysis in Forest Manage ment' and since 1996 extended to the programme 'Economic Optimisation of Multiple-Use Forestry and Other Natural Resources'.
Book Synopsis Transformation and Weighting in Regression by : Raymond J. Carroll
Download or read book Transformation and Weighting in Regression written by Raymond J. Carroll and published by CRC Press. This book was released on 1988-08-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a careful review of the major statistical techniques used to analyze regression data with nonconstant variability and skewness. The authors have developed statistical techniques--such as formal fitting methods and less formal graphical techniques-- that can be applied to many problems across a range of disciplines, including pharmacokinetics, econometrics, biochemical assays, and fisheries research. While the main focus of the book in on data transformation and weighting, it also draws upon ideas from diverse fields such as influence diagnostics, robustness, bootstrapping, nonparametric data smoothing, quasi-likelihood methods, errors-in-variables, and random coefficients. The authors discuss the computation of estimates and give numerous examples using real data. The book also includes an extensive treatment of estimating variance functions in regression.
Book Synopsis Nonparametric Estimation of Weights in Least-squares Regression Analysis by :
Download or read book Nonparametric Estimation of Weights in Least-squares Regression Analysis written by and published by . This book was released on 1978 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings written by and published by . This book was released on 1992 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Second Order Effects in Semiparametric Weighted Least Squares Regression by : Wolfgang K. Härdle
Download or read book Second Order Effects in Semiparametric Weighted Least Squares Regression written by Wolfgang K. Härdle and published by . This book was released on 1988 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Estimation of Linear Models Under Heteroscedasticity by : R. V. S. Prasad
Download or read book Estimation of Linear Models Under Heteroscedasticity written by R. V. S. Prasad and published by LAP Lambert Academic Publishing. This book was released on 2014-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the Present book Chapter I is an introductory one. It contains the general introduction about the problem of heteroscedasticity. Chapter II describes some aspects of linear models with their inferential problems. It deals with some basic statistical results about Gauss-Markov linear model besides the restricted least squares estimation and its application to the tests of general linear hypotheses. Chapter III presents a brief review on the existing estimation methods for linear models under the various specifications of heteroscedastic variances. Chapter IV deals with the analysis and examination of different types of residuals with their applications in the regression analysis. It also contains the restricted residuals in 'Seemingly Unrelated Regression' (SUR) systems. Chapter V proposes some new estimation procedures for linear models under heteroscedasticity. Chapter VI depicts the conclusions .Several references articles regarding the estimation for linear models under heteroscedasticity have been presented under a title "BIBLIOGRAPHY."
