Smooth Distribution Function Estimation for Lifetime Distributions using Szasz-Mirakyan Operators

TL;DR

This paper proposes a new smooth estimator for lifetime distribution functions on the positive real line using Szasz-Mirakyan operators, demonstrating superior asymptotic performance and favorable finite sample results compared to existing methods.

Contribution

Introduces a novel smooth estimator based on Szasz-Mirakyan operators for lifetime distributions, improving upon empirical methods in accuracy and theoretical properties.

Findings

Outperforms empirical distribution function asymptotically

Shows better finite sample performance in simulations

Provides theoretical comparisons favoring the new estimator

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.