Estimating Weights in Heteroscedastic Regression Models by Applying Least Squares to Squared Or Absolute Residuals PDF Download
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Author: Raymond J. Carroll
Publisher:
ISBN:
Category : Calibration
Languages : en
Pages : 26
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Book Description
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).
Author: Raymond J. Carroll
Publisher:
ISBN:
Category : Calibration
Languages : en
Pages : 26
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Book Description
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).
Author: Justine Shults
Publisher: CRC Press
ISBN: 1420099930
Category : Mathematics
Languages : en
Pages : 223
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Book Description
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.
Author: Robert L. Kaufman
Publisher: SAGE Publications
ISBN: 1483322513
Category : Social Science
Languages : en
Pages : 113
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Book Description
This volume 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 book offers three approaches for dealing with heteroskedasticity: variance-stabilizing transformations of the dependent variable; calculating robust standard errors, or heteroskedasticity-consistent standard errors; and 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.
Author: Themba Louis Nyirenda
Publisher:
ISBN:
Category : Homoscedasticity
Languages : en
Pages : 494
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 180
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Book Description
Author: Virendera K. Srivastava
Publisher: CRC Press
ISBN: 9780824776107
Category : Mathematics
Languages : en
Pages : 398
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Book Description
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.
Author: R. V. S. Prasad
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659503450
Category :
Languages : en
Pages : 164
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Book Description
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."
Author: K. Sreenivasulu
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659389726
Category :
Languages : en
Pages : 268
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Book Description
In this some new estimation methods and testing procedures for the linear regression models with heteroscedastic disturbances. A Minimum Norm Quadratic Unbiased (MINQU) estimation method has been developed for estimating the unknown heteroscedastic error variances by using the weighted studentized residuals. A multiplicative heteroscedastic linear regression model has been specified and a method of estimating the parameters of linear regression model along with the in the heteroscedastic error variance has been given by using the predicted residuals. Three types of modified estimators have been proposed for the parameter of multiplicative heteroscedastic error variance by using internally studentized residuals.an adaptive method of estimation has been suggested to estimate the heteroscedastic error variances based on Bartlett's test by using the internally studentized residuals. Besides these new estimation methods, the testing procedures for testing the equality between the regression coefficients in two/sets of linear regression models under heteroscedasticity have been suggested by using the studentized residuals.
Author:
Publisher: SAGE Publications
ISBN: 1544336586
Category : GAUSS
Languages : en
Pages : 273
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Book Description
Least squares estimation.
Author: Wolfgang K. Härdle
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
