Abstract:
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One of the great advantages of shape-constrained methods is that they automatically adapt to the underlying level of smoothness in the true density. For example, if the true density has a linear log-density, the MLE of a log concave density will converge at a nearly parametric rate. This is, of course, a great natural advantage of the methodology. In this work we consider modifications to the log-concave maximum likelihood estimator where most original properties are preserved, while the estimator also converges at nearly parametric rates to the Gaussian density.
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