Shape constrained kernel density estimation |
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Authors: | Melanie Birke |
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Affiliation: | Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany |
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Abstract: | In this paper, a method for estimating monotone, convex and log-concave densities is proposed. The estimation procedure consists of an unconstrained kernel estimator which is modified in a second step with respect to the desired shape constraint by using monotone rearrangements. It is shown that the resulting estimate is a density itself and shares the asymptotic properties of the unconstrained estimate. A short simulation study shows the finite sample behavior. |
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Keywords: | Convexity Log-concavity Monotone rearrangements Monotonicity Nonparametric density estimation |
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