Dipartimento di Scienze Statistiche

PhD program in Statistics DSS Statistics Seminar September 23, 2025, 12:00 In person.Room 24 (CU002) Webinar^.https://uniroma1.zoom.us/j/83625004899?pwd=bXCtz0 mp759PUh2lkqT0BUoVa0Uegg.1 Passcode: 123456   Abstract An Overview of Robust Regression Mixture Models Emphasizing Symmetric α-Stable Distributions Shaho Zarei University of Kurdistan (UOK) The typical method for estimating mixture of regression models relies on the assumption that error components are normally distributed. This assumption makes them highly vulnerable to outliers or data with heavy-tailed errors. This lecture will review some robust alternatives for mixture of regression models. In particular, we will focus on a new robust model introduced by Zarei, which extends the mixture of symmetric α-stable (SαS) distributions to the regression setting. The SαS distribution is a heavy-tailed generalization of the normal distribution, where an additional parameter, α, controls the heaviness of the tails. A unique characteristic of the SαS distribution is that its variance diverges to infinity when α < 2. This property makes the model exceptionally robust against extreme outliers compared to other heavy-tailed distributions, like the Student's t-distribution. The model's parameters, except for α, are estimated using a standard Expectation-Maximization (EM) algorithm. The parameter α is estimated separately via a stochastic EM algorithm that utilizes a rejection sampling method. We will illustrate and compare this new model with existing mixture regression models using both simulated and real-world datasets.