401 – L1 and Other Regression Problems
A Robust Tobit Regression Model When Errors Are from the Epsilon Skew Exponential Power Family
Hassan Elsalloukh
University of Arkansas at Little Rock
Ahmad Flaih
University of Arkansas at Little Rock
Jose Hector Guardiola
Texas A&M University at Corpus Christi
In this paper, we generalize the Epsilon Skew Normal (ESN) Tobit regression model, proposed by Mashtare Jr. and Huston (2011), to the Epsilon Skew Exponential Power (ESEP) Tobit regression, which was proposed by Elsalloukh (2004). Tobit model assumes the normality of residuals term. Elsalloukh et al.(2005) proposed the Epsilon Skew Exponential Power (ESEP) family of distributions which includes the ESN distribution and many others distributions as special cases. This flexible family of distributions can accommodate both heavy tails and skewness behaviors. Therefore, ESEP can be considered as a "robust model" to cope with the deviation from normality. We propose the use of the Epsilon Skew Exponential Power family of distribution as an alternative model to make inference on estimating the interested parameters of the Tobit regression model. In the process, we develop the basic properties of the ESEP Tobit model, such as the structural equation, the expected value of the censored variable, and the loglikelihood functions based on the piecewise nature of the ESEP density.
