Relative error regression function estimation using the Bernstein polynomials approach

This work introduces a different method for estimating the regression function of a response variable Y based on a random variable X, using Bernstein polynomials. If a regression function has bounded support, the kernel estimates often exceed the boundaries and are therefore biased on and near these limits. This new estimator’s construction combines the Bernstein polynomial technique, which addresses edge problems, with relative error estimation to handle the presence of outliers. The estimator is derived by minimizing the mean squared relative error, which is especially advantageous for analyzing data with positive responses. We analyze this estimator’s local and global behavior as it approaches its limits. Simulations are available to illustrate the asymptotic behavior of the estimator when outliers are present. Furthermore, an analysis was performed on specific economic data to demonstrate the robustness of the novel estimator compared to other existing estimators.