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The Derivation of Maximum Likelihood Estimation for Linear Relation with Outliers

Titirut Thipbharos

Abstract


An alternative regression, called adjusted regression, is suggested in this paper. Following two principle methods, namely the method of limitation of regression outlier values at the lower limit or the upper limit of the confidence band for the individual prediction and the piecewise method. This method of adjustment can deal with the outlier problem. In this paper, a likelihood function was constructed, and the parameters of the adjusted regression model were derived by using maximum likelihood estimation. The performance of the adjusted regression was studied by the construction of a linear relationship between characteristic factors and insurance expenditure of Thai farmer households. In particular cases, the adjusted fitting line has a better fit than the piecewise regression.

Keywords


Regression outliers, Confidence band of the individual prediction, Piecewise regression model, Maximum likelihood method.

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