This paper examines the theory of the estimation of econometric models and Hausman tests with sampling weights. The Manski-Lerman weighted conditional MLE is emphasized because of its popularity in econometric estimation with sampling weights. It is an inefficient alternative to full information...

We derive a new inequality for uniform deviations of averages from their means. The inequality is a common generalization of previous results of Vapnik and Chervonenkis (1974) and Pollard (1986). Usingthe new inequality we obtain tight bounds for empirical loss minimization learning