Weighted mixture regression model based on t-distribution in the presence of a leverage point

The Expectation-Maximization (EM) algorithm is an efficient method for estimating the parameters of a mixture regression model in the presence of outliers in the Y-direction. Unfortunately, this method breaks down when leverage points are present in the dataset. The most common procedure used in the literature involves removing leverage points after identifying them with single detection methods. However, some authors have pointed out that single detection methods can be inaccurate and have therefore proposed multiple diagnostic approaches. This manuscript proposes the Weighted EM (WEM) method to address the problem of leverage points without requiring data deletion. Moreover, it builds upon the DRGP (RMVN) framework, which is one of the multiple diagnostic methods. Real data and simulation studies were conducted to evaluate the efficiency of the proposed method compared to existing approaches. The results show that the WEM method is more robust and reliable than other methods, particularly when sample sizes are small.