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Activity Number: 72 - Recent Advances in Nonparametric Statistical Methods II
Type: Contributed
Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #329140 Presentation
Title: Bi-S*-Concave Distribution
Author(s): Nilanjana Laha* and Jon A. Wellner
Companies: University of Washington and University of Washington
Keywords: log-concave; bi-log-concave; s-concave; shape-constraint; semi-parametric
Abstract:

We introduce a new shape-constrained class of univariate distribution functions, the bi-s*-concave class. In parallel to results of D\"umbgen, Kolesnyk, and Wilke [Journal of Statistical Planning and Inference, 184, 2017] for what they called the class of bi-log-concave distribution functions, we show that every s-concave density f has a bi-s*-concave distribution function F. We establish that the Cs\"org\H{o} - R\'ev\'esz constant of F is finite for every bi-s*-concave distribution function where the Cs\"org\H{o} - R\'ev\'esz constant plays an important role in the theory of quantile processes on the real line. We also construct s*-concave confidence bands for F refining some non-parametric confidence bands.


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