Skew-t and Semi-parametric Empirical Likelihoods Versus Parametric Robust Likelihood

Abstract

Likelihood is certainly one of the most important entities for inference. The skew-t is a popular distribution that researchers employ to analyze asymmetric data. This model has parameters for skewness and kurtosis to incorporate asymmetry. We found that the skew-t is unable to provide consistent estimate for the location parameters for model misspecification. The empirical likelihood is a distribution-free approach that allows one to construct likelihood functions without knowing the true underlying distribution for data. The empirical likelihood functions exhibit many properties of the parametric likelihood functions. Alternatively, the robust likelihood is a parametric and yet robust approach. One can conveniently fix a number of parametric likelihood functions to become asymptotically valid. We make a thorough comparison between two model-independent likelihood approaches and recommend using an existing parametric adjusted likelihood approach to analyze data.