Smooth Distribution Function Estimation for Lifetime Distributions using Szasz-Mirakyan Operators
Statistics Theory
2022-07-20 v5 Methodology
Statistics Theory
Abstract
In this paper, we introduce a new smooth estimator for continuous distribution functions on the positive real half-line using Szasz-Mirakyan operators, similar to Bernstein's approximation theorem. We show that the proposed estimator outperforms the empirical distribution function in terms of asymptotic (integrated) mean-squared error, and generally compares favourably with other competitors in theoretical comparisons. Also, we conduct the simulations to demonstrate the finite sample performance of the proposed estimator.
Keywords
Cite
@article{arxiv.2005.09994,
title = {Smooth Distribution Function Estimation for Lifetime Distributions using Szasz-Mirakyan Operators},
author = {Ariane Hanebeck and Bernhard Klar},
journal= {arXiv preprint arXiv:2005.09994},
year = {2022}
}
Comments
Small typo in Theorem 10: Now -1/12 instead of +1/12 in the term of order $m^{-1}$