Large Sample Statistical Inference for Skew-Symmetric Families on the Real Line

Abstract

For a general family of one-dimensional skew-symmetric probability densities, the application of the maximum likelihood method to the estimation of the asymmetry parameter λ is studied. Under mild conditions, the existence and consistency of a sequence {λ̂_n} of maximum likelihood estimators is established, and the limit distributions of {λ̂_n} and the sequence of likelihood ratios are determined under the null hypothesis H₀: λ=0. These latter conclusions, which hold under differential singularity of the likelihood function at λ=0, extend to the present framework results recently obtained for general statistical models with null Fisher information.