Probability density estimation approach in linear regression

Abstract

The purpose of this paper is to study the linear relation between the variable x and y. The proposed method determines the best-fitting line using a probability density estimation. It is shown that the method reduced to least-squares method as the bandwidth is increased and that the line which contains data points more than any other lines do is a best-fitting line as bandwidth is decreased. Also, we have shown that the method is insensitive to a few egregious error in the dependent variable as bandwidth is choosed appropriatly. Consequently, the new method gives a various altemative interpretation of the data as bandwidth varies.