Ann Stat 2018 17;46(5):2125-2152. Epub 2018 Aug 17.
Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong Sar.
We study the nonparametric estimation of a decreasing density function in a general -sample biased sampling model with weight (or bias) functions for = 1, …, . The determination of the monotone maximum likelihood estimator and its asymptotic distribution, except for the case when = 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 and its asymptotic distribution at a fixed point are established in this article. Read More