A comparative study of some estimation methods for parameters and effects of outliers in simple regression model for research on small ruminants

Abstract

This paper investigated estimation methods: least squares method, M-estimation, Theil method, Least Absolute Deviation method to estimate the parameters of simple regression model in situation that the underlying assumptions of least squares estimation are untenable because of outliers. To compare these methods, the effect of chest girth on body weights of German Farm x Hair crossbred kids at weaning period was examined. Chest girth of kids is independent variable and body weight at weaning period is dependent variable in the model. Mean square error and R-2 value are used to evaluate estimator performance. Because two observation values are outliers and the model estimated from this method have minimum mean square error and maximum R-2 value for different sample sizes (n=10, 20, 30 or 50), M-estimation method is proposed to predict the parameters of the model.