Showing papers by "Hammou El Barmi published in 2017"
TL;DR: In this paper, the authors developed new consistent estimators of the distribution functions of two continuous random variables X and Y when X is less peaked than Y. Through simulation studies, they show that their estimators outperform in terms of mean-squared error the estimators proposed in El-Barmi and Mukerjee(2012) for the same problem.
Abstract: A random variable X is said to be less peaked about a point μ than a random variable Y about a point ν, denoted by X⪯pkd(μ, ν)Y, if This paper develops new consistent estimators of the distribution functions of two continuous random variables X and Y when X is less peaked than Y. Through simulation studies, we show that our estimators outperform in terms of mean-squared error the estimators proposed in El Barmi and Mukerjee (2012) for the same problem. To illustrate the theory, an empirical example is presented.
4 citations
TL;DR: In this article, a uniformly strongly consistent least-squares estimator is proposed for nonparametric maximum likelihood estimation, which generalises the model of a convex DF, even allowing for jumps.
Abstract: A life distribution function (DF) F is said to be star-shaped if is nondecreasing on its support. This generalises the model of a convex DF, even allowing for jumps. The nonparametric maximum likelihood estimation is known to be inconsistent. We provide a uniformly strongly consistent least-squares estimator. We also derive the convergence in distribution of the estimator at a point where is increasing using the arg max theorem.