Application of Bernstein Polynomials on Estimating a Distribution and Density Function in a Triangular Array

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

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 2, 1-14

Abstract: Abstract In this paper, we study some asymptotic properties for the Bernstein estimators of the limit distribution function and the limit density function under a triangular sample. Specifically, we obtain the uniform strong consistency, mean squared error (MSE) and mean integrated squared error (MISE) for the resulting estimators. In addition, we give the optimal choice of the bandwidth parameter m in terms of the sample size n, for both the MSE and MISE. Numerical simulations are presented to show that the Bernstein estimators outperform Gaussian kernel estimators in terms of MISE under a triangular sample.

Keywords: Bernstein estimators; Uniform strong consistency; MSE; MISE; Triangular array; 60E05; 62G05; 62G07; 62E20 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10032-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10032-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-023-10032-3

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().