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

Shklyar, Sergiy; Schneeweiß, Hans

doi:10.1016/j.jmva.2004.05.002

Cited by 18 publications

(20 citation statements)

References 11 publications

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“…We need (N) only to prove the corresponding strict order relation. Shklyar and Schneeweiss (2005) have proved a similar result for the log-linear Poisson model, but with different arguments. They were able to compute the ACMs of CS and SS explicitly and they could compare them directly.…”

Section: Introductionmentioning

confidence: 70%

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

Shklyar

Schneeweiß²,

Kukush

2006

Metrika

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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 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.

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Section: Introductionmentioning

confidence: 70%

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

Shklyar

Schneeweiß²,

Kukush

2006

Metrika

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“…An example is the Poisson regression model, cf. [21]. This is another argument which points to SQS as the preferred estimation method.…”

Section: Resultsmentioning

confidence: 99%

“…In several cases this integration can be easily carried out explicitly, leading to closed expressions for m k (x, ). The polynomial and the Poisson model of Section 2 are cases in point [18,21]. Here, however, we do not need explicit formulas for m k or form.…”

Section: Conditioningmentioning

confidence: 99%

“…Since we are here only interested in the regression parameter , we can reduce system (20), (21) to just one (vector-valued) equation forˆ only by solving (21) forˆ givenˆ and substituting the resulting solutionˆ (ˆ ) forˆ in (20). If, for simplicity, we then change the notation by writing v(x,ˆ ) for v(x,ˆ ,ˆ (ˆ )), the estimating equation forˆ becomes…”

Section: The Sqs Estimatormentioning

confidence: 99%

“…But these methods typically yield estimates with larger standard errors than SQS, just because they do not use the information inherent in the regressor distribution, for an example see [21].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

Schneeweiß¹,

Cheng

2006

Journal of Multivariate Analysis

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In a structural measurement error model the structural quasi-score (SQS) estimator is based on the distribution of the latent regressor variable. If this distribution is misspecified, the SQS estimator is (asymptotically) biased. Two types of misspecification are considered. Both assume that the statistician erroneously adopts a normal distribution as his model for the regressor distribution. In the first type of misspecification, the true model consists of a mixture of normal distributions which cluster around a single normal distribution, in the second type, the true distribution is a normal distribution admixed with a second normal distribution of low weight. In both cases of misspecification, the bias, of course, tends to zero when the size of misspecification tends to zero. However, in the first case the bias goes to zero in a flat way so that small deviations from the true model lead to a negligible bias, whereas in the second case the bias is noticeable even for small deviations from the true model.

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Tests for detecting overdispersion in models with measurement error in covariates

Yang

Wong

2015

Statistics in Medicine

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Measurement error in covariates can affect the accuracy in count data modeling and analysis. In overdispersion identification, the true mean-variance relationship can be obscured under the influence of measurement error in covariates. In this paper, we propose three tests for detecting overdispersion when covariates are measured with error: a modified score test and two score tests based on the proposed approximate likelihood and quasi-likelihood, respectively. The proposed approximate likelihood is derived under the classical measurement error model, and the resulting approximate maximum likelihood estimator is shown to have superior efficiency. Simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi-likelihood and other alternatives in terms of empirical power. By analyzing a real dataset containing the health-related quality-of-life measurements of a particular group of patients, we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results.

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

Cited by 18 publications

References 11 publications

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

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

Bias of the structural quasi-score estimator of a measurement error model under misspecification of the regressor distribution

Tests for detecting overdispersion in models with measurement error in covariates

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