Maximum Likelihood Estimation of Replicated Linear Functional Relationship Model

Abstract

This paper discusses the parameter estimates as well as the asymptotic covariance in replicated linear functional relationship model (LFRM). The model is assumed to be balanced and equal in each group. The maximum likelihood estimation is used to estimate four parameters in this model namely the intercept, the slope, and two error variances. Although the closed-form of the estimates is not available, it is shown that the closed-form for the asymptotic covariance matrix of the model using the Fisher Information matrix can be obtained. Using a simulation study, we showed that the estimated values of the parameters are unbiased and consistent suggesting the proposed model’s superiority.