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

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.

Small typo in Theorem 10: Now -1/12 instead of +1/12 in the term of order $m^{-1}$

References in corpus (1)

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

Cited by in corpus (5)

• Asymptotic properties of Dirichlet kernel density estimators
• Asymptotic properties of Bernstein estimators on the simplex
• A study of seven asymmetric kernels for the estimation of cumulative distribution functions
• On the Le Cam distance between Poisson and Gaussian experiments and the asymptotic properties of Szasz estimators
• Smooth Distribution Function Estimation for Lifetime Distributions using Szasz-Mirakyan Operators