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Title:

Quasi Score is more Efficient than Corrected Score in a Polynomial Measurement Error Model

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Quasi score, Corrected score, Polynomial model, Measurement errors, Efficiency, Structural methods, Functional methods

Quasi score, Corrected score, Polynomial model, Measurement errors, Efficiency, Structural methods, Functional methods Minimize

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Title:

Methods for Estimation of Radiation Risk in Epidemiological Studies Accounting for Classical and Berkson Errors in Doses

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With a binary response Y , the dose-response model under consideration is logistic in flavor with pr( Y =1 | D ) = R (1+ R ) -1 , R = Î» 0 + EAR D , where Î» 0 is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as D i mes = f i Q i mes /M i mes...

With a binary response Y , the dose-response model under consideration is logistic in flavor with pr( Y =1 | D ) = R (1+ R ) -1 , R = Î» 0 + EAR D , where Î» 0 is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as D i mes = f i Q i mes /M i mes . Here, Q i mes is the measured content of radioiodine in the thyroid gland of person i at time t mes , M i mes is the estimate of the thyroid mass, and f i is the normalizing multiplier. The Q i and M i are measured with multiplicative errors V i Q and V i M , so that Q i mes = Q i tr V i Q (this is classical measurement error model) and M i tr = M i mes V i M (this is Berkson measurement error model). Here, Q i tr is the true content of radioactivity in the thyroid gland, and M i tr is the true value of the thyroid mass. The error in f i is much smaller than the errors in ( Q i mes , M i mes ) and ignored in the analysis. By means of Parametric Full Maximum Likelihood and Regression Calibration (under the assumption that the data set of true doses has lognormal distribution), Nonparametric Full Maximum Likelihood, Nonparametric Regression Calibration, and by properly tuned SIMEX method we study the influence of measurement errors in thyroid dose on the estimates of Î» 0 and EAR. The simulation study is presented based on a real sample from the epidemiological studies. The doses were reconstructed in the framework of the Ukrainian-American project on the investigation of Post-Chernobyl thyroid cancers in Ukraine, and the underlying subpolulation was artificially enlarged in order to increase the statistical power. The true risk parameters were given by the values to earlier epidemiological studies, and then the binary response was simulated according to the dose-response model. ; Vital and Health Statistics, Berkson measurement error, Chornobyl accident, classical measurement error, estimation of radiation risk, full maximum likelihood estimating procedure, regression calibration, SIMEX estimator, uncertainties in thyroid dose Minimize

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A comparison of asymptotic covariance matrices of three consistent estimators in the Poisson regression model with measurement errors

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We consider a Poisson model, where the mean depends on certain covariates in a log-linear way with unknown regression parameters. Some or all of the covariates are measured with errors. The covariates as well as the measurement errors are both jointly normally distributed, and the error covariance matrix is supposed to be known. Three consistent...

We consider a Poisson model, where the mean depends on certain covariates in a log-linear way with unknown regression parameters. Some or all of the covariates are measured with errors. The covariates as well as the measurement errors are both jointly normally distributed, and the error covariance matrix is supposed to be known. Three consistent estimators of the parameters - the corrected score, a structural, and the quasi-score estimators - are compared to each other with regard to their relative (asymptotic) efficiencies. The paper extends an earlier result for a scalar covariate. Minimize

Year of Publication:

2002-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.de/1661/1/paper_283.pdf ; Shklyar, Sergiy und Schneeweiß, Hans (2002): A comparison of asymptotic covariance matrices of three consistent estimators in the Poisson regression model with measurement errors. Sonderforschungsbereich 386, Discussion Paper 283

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Title:

Comparison of three estimators in Poisson errors-in-variables model with one covariate

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A structural errors-in-variables model is investigated, where the response variable follows a Poisson distribution. Assuming the error variance to be known, we consider three consistent estimators and compare their relative efficiencies by means of their asymptotic covariance matrices. The comparison is made for arbitrary error variances. The st...

A structural errors-in-variables model is investigated, where the response variable follows a Poisson distribution. Assuming the error variance to be known, we consider three consistent estimators and compare their relative efficiencies by means of their asymptotic covariance matrices. The comparison is made for arbitrary error variances. The structural quasi-likelihood (QL) estimator is based on a quasi score function, which is constructed from a conditional mean-variance model. The corrected estimator is based on an error-corrected likelihood score function. The alternative estimator is constructed to remove the asymptotic bias of the naive (i.e., ordinary maximum likelihood) estimator. It is shown that the QL estimator is strictly more efficient than the alternative estimator, and the latter one is strictly more efficient than the corrected estimator. Minimize

Year of Publication:

2002-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

DDC:

519 Probabilities & applied mathematics *(computed)* ; 310 Collections of general statistics *(computed)*

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http://epub.ub.uni-muenchen.de/1671/1/paper_293.pdf ; Kukush, Alexander und Shklyar, Sergiy (2002): Comparison of three estimators in Poisson errors-in-variables model with one covariate. Sonderforschungsbereich 386, Discussion Paper 293

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Title:

Quasi Score is more efficient than Corrected Score in a polynomial measurement error model

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We consider a polynomial regression model, where the covariate is measured with Gaussian errors. The measurement error variance is supposed to be known. The covariate is normally distributed with known mean and variance. Quasi Score (QS) and Corrected Score (CS) are two consistent estimation methods, where the first makes use of the distribution...

We consider a polynomial regression model, where the covariate is measured with Gaussian errors. The measurement error variance is supposed to be known. The covariate is normally distributed with known mean and variance. Quasi Score (QS) and Corrected Score (CS) are two consistent estimation methods, where the first makes use of the distribution of the covariate (structural method), while the latter does not (functional method). It may therefore be surmised that the former method is (asymptotically) more efficient than the latter one. This can, indeed, be proved for the regression parameters. We do this by introducing a third, so-called Simple Score (SS),estimator, the efficiency of which turns out to be intermediate between QS and CS. When one includes structural and functional estimators for the variance in the equation, SS is still more efficient than CS. When the mean and variance of the covariate are not known and have to be estimated as well, one can still maintain that QS is more efficient than SS for the regression parameters. Minimize

Publisher:

Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München

Year of Publication:

2005

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310 ; Quasi Score ; Corrected Score ; Polynomial Model ; Measurement Errors ; Efficiency ; Structural Methods ; Functional Methods

ddc:310 ; Quasi Score ; Corrected Score ; Polynomial Model ; Measurement Errors ; Efficiency ; Structural Methods ; Functional Methods Minimize

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http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 445

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Title:

Quasi Score is more efficient than Corrected Score in a general nonlinear measurement error model

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Techn. Univ.; Sonderforschungsbereich 386, Statistische Analyse Diskreter Strukturen München

Year of Publication:

2005

Document Type:

doc-type:workingPaper

Language:

eng

Subjects:

ddc:310

ddc:310 Minimize

Rights:

http://www.econstor.eu/dspace/Nutzungsbedingungen

http://www.econstor.eu/dspace/Nutzungsbedingungen Minimize

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Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 451

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Title:

Approximation of fractional Brownian motion by martingales

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We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given. Minimize

Year of Publication:

2012-05-21

Document Type:

text

Subjects:

Mathematics - Probability ; 60G22 ; 60G44 ; 90C25

Mathematics - Probability ; 60G22 ; 60G44 ; 90C25 Minimize

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Title:

Quasi Score is more efficient than Corrected Score in a polynomial measurement error model

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Description:

We consider a polynomial regression model, where the covariate is measured with Gaussian errors. The measurement error variance is supposed to be known. The covariate is normally distributed with known mean and variance. Quasi Score (QS) and Corrected Score (CS) are two consistent estimation methods, where the first makes use of the distribution...

We consider a polynomial regression model, where the covariate is measured with Gaussian errors. The measurement error variance is supposed to be known. The covariate is normally distributed with known mean and variance. Quasi Score (QS) and Corrected Score (CS) are two consistent estimation methods, where the first makes use of the distribution of the covariate (structural method), while the latter does not (functional method). It may therefore be surmised that the former method is (asymptotically) more efficient than the latter one. This can, indeed, be proved for the regression parameters. We do this by introducing a third, so-called Simple Score (SS), estimator, the efficiency of which turns out to be intermediate between QS and CS. When one includes structural and functional estimators for the variance of the error in the equation, SS is still more efficient than CS. When the mean and variance of the covariate are not known and have to be estimated as well, one can still maintain that QS is more efficient than SS for the regression parameters. Minimize

Year of Publication:

2005-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Language:

eng

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

Relations:

http://epub.ub.uni-muenchen.de/1814/1/paper_445.pdf ; Shklyar, Sergiy und Schneeweiß, Hans und Kukush, Alexander (2005): Quasi Score is more efficient than Corrected Score in a polynomial measurement error model. Sonderforschungsbereich 386, Discussion Paper 445

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Title:

Quasi Score is more efficient than Corrected Score in a general nonlinear measurement error model

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We compare two consistent estimators of the parameter vector beta of a general exponential family measurement error model with respect to their relative efficiency. The quasi score (QS) estimator uses the distribution of the regressor, the corrected score (CS) estimator does not make use of this distribution and is therefore more robust. However...

We compare two consistent estimators of the parameter vector beta of a general exponential family measurement error model with respect to their relative efficiency. The quasi score (QS) estimator uses the distribution of the regressor, the corrected score (CS) estimator does not make use of this distribution and is therefore more robust. However, if the regressor distribution is known, QS is asymptotically more efficient than CS. In some cases it is, in fact, even strictly more efficient, in the sense that the difference of the asymptotic covariance matrices of CS and QS is positive definite. Minimize

Year of Publication:

2005-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

Relations:

http://epub.ub.uni-muenchen.de/1820/1/paper_451.pdf ; Kukush, Alexander und Schneeweiß, Hans und Shklyar, Sergiy (2005): Quasi Score is more efficient than Corrected Score in a general nonlinear measurement error model. Sonderforschungsbereich 386, Discussion Paper 451

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Title:

Methods for Estimation of Radiation Risk in Epidemiological Studies Accounting for Classical and Berkson Errors in Doses

Author:

Description:

With a binary response Y, the dose-response model under consideration is logistic in flavor with pr(Y=1 | D) = R (1+R)−1, R = λ0 + EAR D, where λ0 is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as Dimes=fiQimes/Mimes. Here, Qimes is the measured content of radio...

With a binary response Y, the dose-response model under consideration is logistic in flavor with pr(Y=1 | D) = R (1+R)−1, R = λ0 + EAR D, where λ0 is the baseline incidence rate and EAR is the excess absolute risk per gray. The calculated thyroid dose of a person i is expressed as Dimes=fiQimes/Mimes. Here, Qimes is the measured content of radioiodine in the thyroid gland of person i at time tmes, Mimes is the estimate of the thyroid mass, and fi is the normalizing multiplier. The Qi and Mi are measured with multiplicative errors ViQ and ViM, so that Qimes=QitrViQ (this is classical measurement error model) and Mitr=MimesViM (this is Berkson measurement error model). Here, Qitr is the true content of radioactivity in the thyroid gland, and Mitr is the true value of the thyroid mass. The error in fi is much smaller than the errors in ( Qimes, Mimes) and ignored in the analysis. Minimize

Publisher:

Berkeley Electronic Press

Year of Publication:

2011-02-16

Document Type:

Text

Language:

en

Subjects:

Article

Article Minimize

Rights:

Copyright © 2011 The Berkeley Electronic Press. All rights reserved

Copyright © 2011 The Berkeley Electronic Press. All rights reserved Minimize

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