ESTIMATION OF A MONOTONE DENSITY IN S-SAMPLE BIASED SAMPLING MODELS.

ABSTRACT: We study the nonparametric estimation of a decreasing density function g 0 in a general s-sample biased sampling model with weight (or bias) functions wi for i = 1, …, s. The determination of the monotone maximum likelihood estimator ?n and its asymptotic distribution, except for the case when s = 1, has been long missing in the literature due to certain non-standard structures of the likelihood function, such as non-separability and a lack of strictly positive second order derivatives of the negative of the log-likelihood function. The existence, uniqueness, self-characterization, consistency of ?n and its asymptotic distribution at a fixed point are established in this article. To overcome the barriers caused by non-standard likelihood structures, for instance, we show the tightness of ?n via a purely analytic argument instead of an intrinsic geometric one and propose an indirect approach to attain the n -rate of convergence of the linear functional ? wi ?n.

SUBMITTER: Chan KCG 

PROVIDER: S-EPMC6251412 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature