In this survey, we evaluate estimators by comparing their asymptotic variances. The role of the efficiency bound, in this context, is to give a lower bound to the asymptotic variance of an estimator. An estimator with asymptotic variance equal to the efficiency bound can therefore be said to be...

Abstract We introduce a notion of median uncorrelation that is a natural extension of mean (linear) uncorrelation. A scalar random variable Y is median uncorrelated with a k-dimensional random vector X if and only if the slope from an LAD regression of Y on X is zero. Using this simple...

Let Y denote an n x 1 vector of observations such that Y = [mu] + [sigma][var epsilon] where [mu] is an unknown n x 1 vector, [sigma] 0 is an unknown parameter, and [var epsilon] is an n x 1 vector of independent standard normal random variables. A linear regression analysis is often based on a...

Consider a model with parameter θ = (ψ, λ), where ψ is the parameter of interest, and let L(ψ, λ) denote the likelihood function. One approach to likelihood inference for ψ is to use an integrated likelihood function, in which λ is eliminated from L(ψ, λ) by integrating with respect to...

It is well-known that in a given decision problem if T is a sufficient statistic then given any decision function there exists an equivalent decision function that depends on the sample point only through T. In this note, it is shown that the same result does not hold if conditional inference is...