應用拉普拉斯分佈於改變點迴歸模型估計之研究

This report proposes a robust procedure for solving switching regression problems. The proposed method is generally enough to deal with data contaminated by atypical observations due to measurement errors or drawn from heavy-tailed distributions. The robustness is achieved by assuming the regression errors have Laplace distributions. We consider the switch points as the latent class variables so that the switching regression model turns into a mixture model. We employ the expectation and maximization to derive the maximum likelihood estimators of the switch points and regression parameters simultaneously. A simulation study shows the efficiency and effectiveness of the proposed method. The superiority of the proposed algorithm is demonstrated experiments with numerical and real examples. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. The resistance to high leverage outliers is particularly important due to their devastating effect on the fit of regression models to data. The practicability of the proposed approach is shown by real data.