Application of the Maximum Likelihood Approach to Estimation of Polynomial Regression Model

Abstract

The ordinary least squares (OLS) method had been extensively applied to estimation of different classes of regression model under specific assumptions. However, this estimation procedure OLS does not perform well with outliers and small sample sizes. As a result, this work considered the application of the maximum likelihood method for polynomial regression model using sample sizes as against the large sample assumption in OLS. The efficiency of the maximum likelihood (ML) estimation technique was put to test by comparing its model fit to that of the OLS using some real world data sets. The results of analysis of these data sets using both methods showed that the ML outperformed the OLS since it gave better estimates with lower mean square error (MSE) values in all the four data sets considered and higher coefficient of determination (R2) values. Although, both methods resulted in overall good fit, but the ML is more efficient than the OLS because it resulted in lower MSE for small sample sizes.