We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a
log-concave density, ie a density of the form f 0= exp ϕ 0 where ϕ 0 is a concave function on …

Although a natural measure of the central tendency of a sample of continuous data is its
mode the mean and median are the most popular measures of location due to their …

We consider the non-parametric maximum likelihood estimation in the class of Polya
frequency functions of order two, viz. the densities with a concave logarithm. This is a …

We study the statistical properties of the least squares estimator in unimodal sequence
estimation. Although closely related to isotonic regression, unimodal regression has not …

Bayesian semiparametric models for mean and median regressions abound, but a void for
mode regressions exists. We fill this gap by nonparametrically modeling the error distribution …

Consider an Internet file for which data on last time of access/modification (A/M) of the file
are collected at periodic intervals, but for which direct A/M data are not available …

It is well known that the unimodal maximum likelihood estimator of a density is consistent
everywhere but at the mode. The authors review various ways to solve this problem and …

We study the statistical properties of the least squares estimator in unimodal sequence
estimation. Although closely related to isotonic regression, unimodal regression has not …

Given assumptions about shape and smoothness, a density is estimated non-parametrically
using regression splines. Examples of shapes include decreasing, decreasing and convex …

Measures of central tendency have been widely used for summarising statistical data, with
the mean being the most popular summary statistic. However, in reallife applications it is not …