Abstract
Bounds for the bracketing entropy of the classes of bounded k-monotone functions on [0, A] are obtained under both the Hellinger distance and the L p(Q) distance, where 1 ⩽ p < ∞ and Q is a probability measure on [0,A]. The result is then applied to obtain the rate of convergence of the maximum likelihood estimator of a k-monotone density.
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This work was supported by National Science Foundation of USA (Grant No. DMS-0405855, DMS-0804587)
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Gao, F., Wellner, J.A. On the rate of convergence of the maximum likelihood estimator of a k-monotone density. Sci. China Ser. A-Math. 52, 1525–1538 (2009). https://doi.org/10.1007/s11425-009-0102-y
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DOI: https://doi.org/10.1007/s11425-009-0102-y