2020/11/15 by Mehrdad Naderi, Elham Mirfarah, Naderi, Mehrdad +6
Computer Science · Decision Sciences · Mathematics · #62E15 #62J20 #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Other Statistics (stat.OT) #Probabilistic and Robust Engineering Design #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #msc:62E15 #msc:62J20 #stat.CO #stat.ME #stat.OT #stat.TH
paper · pdf · doi:10.48550/arxiv.2011.07559
17 page, 4 figures
arxiv created 2020/11/15 · openalex publication_date 2020/11/15 · arxiv updated 2020/11/17 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
In the framework of censored data modeling, the classical linear regression model that assumes normally distributed random errors has received increasing attention in recent years, mainly for mathematical and computational convenience. However, practical studies have often criticized this linear regression model due to its sensitivity to departure from the normality and from the partial nonlinearity. This paper proposes to solve these potential issues simultaneously in the context of the partial linear regression model by assuming that the random errors follow a scale-mixture of normal (SMN) family of distributions. The proposed method allows us to model data with great flexibility, accommodating heavy tails, and outliers. By implementing the B-spline function and using the convenient hierarchical representation of the SMN distributions, a computationally analytical EM-type algorithm is developed to perform maximum likelihood inference of the model parameters. Various simulation studies are conducted to investigate the finite sample properties as well as the robustness of the model in dealing with the heavy-tails distributed datasets. Real-word data examples are finally analyzed for illustrating the usefulness of the proposed methodology.