Asymptotic Results on a General Class of Empirical Statistics: Power and Confidence Interval Properties

Authors: Chang, In; Mukerjee, Rahul

Source: Annals of the Institute of Statistical Mathematics, Volume 58, Number 3, September 2006 , pp. 427-440(14)

Publisher: Springer

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Abstract:

We consider a very general class of empirical statistics that includes (a) empirical discrepancy (ED) statistics, (b) generalized empirical exponential family likelihood statistics, (c) generalized empirical likelihood statistics, (d) empirical statistics arising from Bayesian considerations, and (e) Bartlett-type adjusted versions of ED statistics. With reference to this general class, we investigate higher order asymptotics on power and expected lengths of confidence intervals. For (b)-(e), such results have been hitherto unexplored. Furthermore, our findings help in understanding the presently known results on the subclass (a) from a wider perspective.

Keywords: Average power; Bartlett-type adjustment; Confidence interval; Contiguous alternatives; Edgeworth expansion; Empirical likelihood; Minimaxity; Second-order; Third-order

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10463-006-0040-1

Affiliations: 1: Email: rmuk1@hotmail.com

Publication date: 2006-09-01