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...

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense...

<p>The main objective of this paper is to derive the efficiency bounds for estimating certain linear functionals of an unknown structural function when the latter is not itself a conditional expectation.

Let Y=μ∗(X)+ε, where μ∗ is unknown and E[ε|X]≠0 with positive probability but there exist instrumental variables W such that E[ε|W]=0 w.p.1. It is well known that such nonparametric regression models are generally “ill-posed” in the sense that the map from the data to μ∗ is not...

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a...

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...

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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...