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 Lp(Q) distance,where 1 p < ∞ and Q is a probability measure on [0,A]...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 Lp(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.展开更多
基金supported by National Science Foundation of USA (Grant No.DMS-0405855,DMS-0804587)
文摘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 Lp(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.
