This paper provides a set of uniform consistency results with rates for non- parametric density and regression estimators smoothed by the beta kernel hav- ing support on the unit interval. Weak and strong uniform convergence is explored on the basis of expanding compact sets and general sequences of smoothing parameters. The results in this paper are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel esti- mate as a plug-in. We provide simulations and a real data example illustrating attractive properties of the estimator.
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