Weighted fast-trimmed likelihood estimator for mixture regression models

Abstract

The fast-trimmed likelihood estimate is a robust method to estimate the parameters of a mixture regression model. However, this method is vulnerable to the presence of bad leverage points, which are outliers in the direction of independent variables. To address this issue, we propose the weighted fast-trimmed likelihood estimate to mitigate the impact of leverage points. The proposed method applies the weights of the minimum covariance determinant to the rows suspected of containing leverage points. Notably, both real data and simulation studies were considered to determine the efficiency of the proposed method compared to the previous methods. The results reveal that the weighted fast-trimmed estimate method is more robust and reliable than the fast-trimmed likelihood estimate and the expectation–maximization (EM) methods, particularly in cases with small sample sizes.