Abstract
This paper investigates some properties of the mixture models from the quantile residual life perspective. It is shown that a mixture model is bounded by its components via the quantile residual life. We investigate how mixture models are ordered in terms of the quantile residual life function when their components are ordered. Besides, we prove that the limiting quantile residual life of a mixture is similar to that of the greatest component at infinity. Based on these results, it is possible to construct estimators of two quantile residual life functions subject to an order restriction. Such estimators are shown to be strongly uniformly consistent and asymptotically unbiased. We develop the weak convergence theory for these estimators. Simulations seem to indicate that both of the restricted estimators improve on the empirical (unrestricted) estimators in terms of the mean squared error, uniformly at all quantiles, and for a variety of distributions.
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