Invariant Estimation of Location and Scale Parameters in Generalized Skew-Symmetric Distributions

• Activity Number: 172
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Nelis Potgieter*+ and Marc G. Genton
• Companies: Texas A & M University and Texas A & M University
• Keywords: skew-normal ; skew-t ; characteristic function ; root selection

Abstract

In generalized skew-symmetric models, it is of interest to estimate the location and scale parameters without assuming a specific parametric form for the skewing function. In considering this problem, it has been established that the there are typically multiple solutions for the parameters of interest. The problem of selecting the "correct" root has only been solved satisfactorily in a few cases. We present a new method for estimting the parameters, namely using a distance function based on the real parts of the empirical and true characteristic functions. We proceed to show that the multiple roots that occur are a result of an identifiability issue with the fully generalized skew-symmetric model. Making an additional assumption regarding the behaviour of the skewing function in a region around the origin, this can be overcome. Theoretical and Monte Carlo standard errors for the parameter estimates are used to compare the new method to existing methods.