Corrected score estimators in multivariate regression models with heteroscedastic measurement errors
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2016
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2559
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103 leaves
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b196946
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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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National Institute of Development Administration. Library and Information Center
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Wannaporn Junthopas (2016). Corrected score estimators in multivariate regression models with heteroscedastic measurement errors. Retrieved from: https://repository.nida.ac.th/handle/662723737/5225.
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Corrected score estimators in multivariate regression models with heteroscedastic measurement errors
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Abstract
In this study, the knowledge of parameter estimation theory based on the
corrected score (CS) approach is extended in a linear multivariate multiple regression
model with heteroscedastic measurement errors (HME) and an unknown HME
variance. The heteroscedasticity of the HME variance is assumed to be capable of
being grouped into similar patterns where the sample of observations are assembled
into several sub-samples with the property that the variances of the measurement error
(ME) are homoscedastic within a group but heteroscedastic between groups. In each
group, the variance of the ME of the surrogate variable is estimated by the pooled
variance of the variable with HMEs observed in repeated measurements.
The statistical properties of the proposed CS estimator are analytically investigated based on the specific model in which there are two independent variables of which one is measured with HME. To evaluate the performance of the proposed CS estimator via a simulation study, datasets are generated based on two forms of heteroscedasticity: the step-up function form and the step-down function form. From the simulation results, the ordinary least squares (OLS) estimation of the parameters of the precisely observed variable is unaffected by HME, but the parameter estimators of the variable measured with HME are underestimated. The CS method outperforms the OLS method since the absolute bias and mean square error of the CS estimator are less than those of the OLS estimator when either the number of repeated measurements or the sample size increases, and the bias of the CS estimator approaches zero when the sample size increases. The results of the simulation study show conformance to the theoretical proof
The statistical properties of the proposed CS estimator are analytically investigated based on the specific model in which there are two independent variables of which one is measured with HME. To evaluate the performance of the proposed CS estimator via a simulation study, datasets are generated based on two forms of heteroscedasticity: the step-up function form and the step-down function form. From the simulation results, the ordinary least squares (OLS) estimation of the parameters of the precisely observed variable is unaffected by HME, but the parameter estimators of the variable measured with HME are underestimated. The CS method outperforms the OLS method since the absolute bias and mean square error of the CS estimator are less than those of the OLS estimator when either the number of repeated measurements or the sample size increases, and the bias of the CS estimator approaches zero when the sample size increases. The results of the simulation study show conformance to the theoretical proof
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Thesis (Ph.D. Statistics))--National Institute of Development Administration, 2016