On the Rates of Asymptotic Normality for Bernstein Polynomial Estimators in a Triangular Array

Dawei Lu () and Lina Wang ()
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Dawei Lu: Dalian University of Technology
Lina Wang: Dalian University of Technology

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1519-1536

Abstract: Abstract It is well known that the empirical distribution function has superior properties as an estimator of the underlying distribution function F. However, considering its jump discontinuities, the estimator is limited when F is continuous. Mixtures of the binomial probabilities relying on Bernstein polynomials lead to good approximation properties for the resulting estimator of F. In this paper, we establish the rates of (pointwise) asymptotic normality for Bernstein estimators by the Berry-Esseen Theorem in the case that the observations are in a triangular array. Particularly, the (asymptotic) absence of the boundary bias and the asymptotic behaviors of the variance are investigated. Besides, numerical simulations are presented to verify the validity of our main results.

Keywords: Bernstein polynomials; Distribution function estimator; Asymptotic normality; Berry-Esseen Theorem; Triangular array; 60F05; 62G05; 62G30 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09829-3

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