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Two steps generalized maximum entropy estimation procedure for fitting linear regression when both covariates are subject to error

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  • Amjad D. Al-Nasser

Abstract

This paper presents a procedure utilizing the generalized maximum entropy (GME) estimation method in two steps to quantify the uncertainty of the simple linear structural measurement error model parameters exactly. The first step estimates the unknowns from the horizontal line, and then the estimates were used in a second step to estimate the unknowns from the vertical line. The proposed estimation procedure has the ability to minimize the number of unknown parameters in formulating the GME system within each step, and hence reduce variability of the estimates. Analytical and illustrative Monte Carlo simulation comparison experiments with the maximum likelihood estimators and a one-step GME estimation procedure were presented. Simulation experiments demonstrated that the two steps estimation procedure produced parameter estimates that are more accurate and more efficient than the classical estimation methods. An application of the proposed method is illustrated using a data set gathered from the Centre for Integrated Government Services in Delma Island - UAE to predict the association between perceived quality and the customer satisfaction.

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  • Amjad D. Al-Nasser, 2014. "Two steps generalized maximum entropy estimation procedure for fitting linear regression when both covariates are subject to error," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1708-1720, August.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:8:p:1708-1720
    DOI: 10.1080/02664763.2014.888544
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    References listed on IDEAS

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    1. Jinhong You & Haibo Zhou, 2007. "On Semiparametric EV Models with Serially Correlated Errors in Both Regression Models and Mismeasured Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 365-383, June.
    2. Mohammad Al-Rawwash & Amjad D. Al-Nasser, 2013. "Repeated measures and longitudinal data analysis using higher-order entropies," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(1), pages 100-111, February.
    3. Hengjian Cui & Efang Kong, 2006. "Empirical Likelihood Confidence Region for Parameters in Semi‐linear Errors‐in‐Variables Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 153-168, March.
    4. Enrico Ciavolino & Amjad Al-Nasser, 2009. "Comparing generalised maximum entropy and partial least squares methods for structural equation models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(8), pages 1017-1036.
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