On Bernstein polynomial estimators of the hazard rate function

Abstract

For the density and distribution functions supported on the unit interval, Bernstein polynomial estimators are known to have good asymptotic properties under appropriate regularity conditions on the function to be estimated. In particular, these estimators are asymptotically unbiased over the entire unit interval. In this paper, we consider the estimation method using Bernstein polynomials and we show that it can be naturally adapted to the hazard function. The asymptotic properties of the obtained estimators are studied. More precisely, we obtain strong consistency and asymptotic normality under appropriate assumptions.