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.
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