Inference on Mixtures Under Tail Restrictions
16 Pages Posted: 4 Dec 2013
Date Written: December 3, 2013
Two-component mixtures are nonparametrically identified under tail-dominance conditions on the component distributions if a source of variation is available that affects the mixing proportions but not the component distributions. We motivate these restrictions through several examples. One interesting example is a location model where the location parameter is subject to classical measurement error. The identification analysis suggests very simple closed-form estimators of the component distributions and mixing proportions based on ratios of intermediate quantiles. We derive their asymptotic properties using results on tail empirical processes, and we provide simulation evidence on their finite-sample performance.
Keywords: mixture model, nonparametric identification and estimation, tail empirical process
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