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VOL. 57 | 2009 Large Sample Statistical Inference for Skew-Symmetric Families on the Real Line


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 {λ̂n} of maximum likelihood estimators is established, and the limit distributions of {λ̂n} 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.


Published: 1 January 2009
First available in Project Euclid: 3 August 2009

zbMATH: 1271.62032
MathSciNet: MR2681677

Digital Object Identifier: 10.1214/09-LNMS5717

Primary: 62F10
Secondary: 62F12

Rights: Copyright © 2009, Institute of Mathematical Statistics


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