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

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.