TITLE:
Some Likelihood Based Properties in Large Samples: Utility and Risk Aversion, Second Order Prior Selection and Posterior Density Stability
AUTHORS:
Michael Brimacombe
KEYWORDS:
Arrow-Pratt Theorem, Expected Utility, Information Similar Priors, Likelihood Function, Prior Stability, Score Function, Risk Aversion
JOURNAL NAME:
Open Journal of Statistics,
Vol.6 No.6,
December
2,
2016
ABSTRACT: The likelihood function plays a central
role in statistical analysis in relation to information, from both frequentist
and Bayesian perspectives. In large samples several new properties of the
likelihood in relation to information are developed here. The Arrow-Pratt
absolute risk aversion measure is shown to be related to the Cramer-Rao Information
bound. The derivative of the log-likelihood function is seen to provide a
measure of information related stability for the Bayesian posterior density. As
well, information similar prior densities can be defined reflecting the central
role of likelihood in the Bayes learning paradigm.