On the boundary properties of Bernstein polynomial estimators of density and distribution functions |
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Authors: | Alexandre Leblanc |
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Affiliation: | Department of Statistics, University of Manitoba, Winnipeg, Canada R3T 2N2 |
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Abstract: | For density and distribution functions supported on [0,1], Bernstein polynomial estimators are known to have optimal mean integrated squared error (MISE) properties under the usual smoothness conditions on the function to be estimated. These estimators are also known to be well-behaved in terms of bias: they have uniform bias over the entire unit interval. What is less known, however, is that some of these estimators do experience a boundary effect, but of a different nature than what is seen with the usual kernel estimators. |
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Keywords: | Bernstein polynomials Density estimation Mean squared error Distribution function Asymptotic properties Boundary bias |
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