Properties of Estimators of Errors-in-variables Regression Models PDF Download

Author: Paul P. Gallo
Publisher:
ISBN:
Category : Error analysis (Mathematics)
Languages : en
Pages : 121

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Author: Philip J. Brown
Publisher: American Mathematical Soc.
ISBN: 0821851179
Category : Mathematics
Languages : en
Pages : 262

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Book Description
Measurement error models describe functional relationships among variables observed, subject to random errors of measurement. This book treats general aspects of the measurement problem and features a discussion of the history of measurement error models.

Author: Denzil G. Fiebig
Publisher:
ISBN:
Category : Least squares
Languages : en
Pages : 44

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Author: Shu Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
There has been a continuing interest among statisticians in the problem of regression models wherein the independent variables are measured with error and there is considerable literature on the subject. In the following report, we discuss the errors-in-variables regression model: yi = [Beta]0 + [Beta]1xi + [Beta]2zi + [Epsilon]i, Xi = xi + ui, Zi = zi + vi with i.i.d. errors ([Epsilon]i, ui, vi), for i = 1, 2 ..., n and find the least square estimators for the parameters of interest. Both weak and strong consistency for the least square estimators [b̂eta]0, [b̂eta]1, and [b̂eta]2 of the unknown parameters [Beta]0, [Beta]1, and [Beta]2 are obtained. Moreover, under regularity conditions, the asymptotic normalities of the estimators are reported.

Author: William Edwards Deming
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 298

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Book Description
Introduction to basic concepts of statistics, curve fitting, least squares solution, conditions without parameter, conditions containing parameters. 26 exercises worked out.

Author: Rolla Edward Park
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 54

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Book Description
A Monte Carlo study is made of the small sample properties of various estimators of the linear regression model with first-order autocorrelated errors. When independent variables are trended, estimators using T transformed observations (Prais-Winsten) are much more efficient than those using T-1 (Cochrane-Orcutt). The best of the feasible estimators is iterated Prais-Winsten using a sum-of-squared-error minimizing estimate of the autocorrelation coefficient rho. None of the feasible estimators performs well in hypothesis testing; all seriously underestimate standard errors, making estimated coefficients appear to be much more significant than they actually are. (Author).

Author: P.A.V.B. Swamy
Publisher: Springer Science & Business Media
ISBN: 3642806538
Category : Business & Economics
Languages : en
Pages : 219

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Book Description
This short monograph which presents a unified treatment of the theory of estimating an economic relationship from a time series of cross-sections, is based on my Ph. D. dissertation submitted to the University of Wisconsin, Madison. To the material developed for that purpose, I have added the substance of two subsequent papers: "Efficient methods of estimating a regression equation with equi-correlated disturbances", and "The exact finite sample properties of estimators of coefficients in error components regression models" (with Arora) which form the basis for Chapters 11 and III respectively. One way of increasing the amount of statistical information is to assemble the cross-sections of successive years. To analyze such a body of data the traditional linear regression model is not appropriate and we have to introduce some additional complications and assumptions due to the hetero geneity of behavior among individuals. These complications have been discussed in this monograph. Limitations of economic data, particularly their non-experimental nature, do not permit us to know a priori the correct specification of a model. I have considered several different sets of assumptionR about the stability of coeffi cients and error variances across individuals and developed appropriate inference procedures. I have considered only those sets of assumptions which lead to opera tional procedures. Following the suggestions of Kuh, Klein and Zellner, I have adopted the linear regression models with some or all of their coefficients varying randomly across individuals.

Author: Raymond J. Carroll
Publisher:
ISBN:
Category : Monte Carlo method
Languages : en
Pages : 28

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Book Description
This report studies the functional errors-in-variables regression model. In the case of no equation error (all randomness due to measurement errors), the maximum likelihood estimator computed assuming normality is asymptotically better than the usual moments estimator, even if the errors are not normally distributed. For certain statistical problems such as randomized two group analysis of covariance, the least squares estimate is shown to be better than the aformentioned errors-in-variables methods for estimating certain important contrasts.

Author: Marie Davidian
Publisher: Springer
ISBN: 3319058010
Category : Mathematics
Languages : en
Pages : 599

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Book Description
This volume contains Raymond J. Carroll's research and commentary on its impact by leading statisticians. Each of the seven main parts focuses on a key research area: Measurement Error, Transformation and Weighting, Epidemiology, Nonparametric and Semiparametric Regression for Independent Data, Nonparametric and Semiparametric Regression for Dependent Data, Robustness, and other work. The seven subject areas reviewed in this book were chosen by Ray himself, as were the articles representing each area. The commentaries not only review Ray’s work, but are also filled with history and anecdotes. Raymond J. Carroll’s impact on statistics and numerous other fields of science is far-reaching. His vast catalog of work spans from fundamental contributions to statistical theory to innovative methodological development and new insights in disciplinary science. From the outset of his career, rather than taking the “safe” route of pursuing incremental advances, Ray has focused on tackling the most important challenges. In doing so, it is fair to say that he has defined a host of statistics areas, including weighting and transformation in regression, measurement error modeling, quantitative methods for nutritional epidemiology and non- and semiparametric regression.

Author: Lawrence
Publisher: CRC Press
ISBN: 9780824781293
Category : Mathematics
Languages : en
Pages : 320

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Book Description
Combining theory, methodology, and applications in a unified survey, this important reference/text presents the most recent results in robust regression analysis, including properties of robust regression techniques, computational issues, forecasting, and robust ridge regression. It provides useful case studies so that students and engineers can apply these techniques to forecasting, quantitative business analysis, econometrics, marketing, statistics, and demand modeling. Robust Regression: Analysis and Applications characterizes robust estimators in terms of how much they weight each observation ... discusses generalized properties of L[subscript p]-estimators ... includes an algorithm for identifying outliers using least absolute value criterion in regression modeling ... reviews redescending M-estimators ... studies L[subscript 1] linear regression ... proposes the best linear unbiased estimators for fixed parameters and random errors in the mixed linear model ... summarizes known properties of L[subscript 1] estimators for time series analysis ... examines ordinary least squares, latent root regression, and a robust regression weighting scheme ... and evaluates results from five different robust ridge regression estimators. Containing 120 tables and diagrams plus numerous bibliographic citations, Robust Regression: Analysis and Applications is the leading reference for applied statisticians, operations researchers, econometricians, marketing forecasters, business administration and management scientists, and industrial engineers as well as a text for graduate statistics or economics courses. Book jacket.