Online Program Home
My Program

Abstract Details

Activity Number: 584 - Advances in Semi- and Nonparametric Statistical Analysis
Type: Contributed
Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #330387 Presentation
Title: ESTIMATION of a MONOTONE DENSITY in S-SAMPLE BIASED SAMPLING MODELS
Author(s): Hok Kan Ling* and Kwun Chuen Gary Chan and Tony Sit and Sheung Chi Phillip Yam
Companies: Columbia University and University of Washington and The Chinese University of Hong Kong and The Chinese University of Hong Kong
Keywords: shape-constrained; nonparametric estimation; biased sampling; density estimation
Abstract:

We study the nonparametric estimation of a decreasing density function in a general s-sample biased sampling model. The determination of the monotone maximum likelihood estimator (monotone MLE) 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 the monotone MLE 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 the monotone MLE via a purely analytic argument instead of an intrinsic geometric one and propose an indirect approach to attain the rate of convergence of certain linear functionals involved in the likelihood.


Authors who are presenting talks have a * after their name.

Back to the full JSM 2018 program