Recursive density estimators based on Robbins–Monro’s scheme and using Bernstein polynomials

Slaoui, Yousri; Jmaei, Asma

doi:10.4310/sii.2019.v12.n3.a8

Cited by 24 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where F n is the empirical distribution function and b k (m, x) = C k m x k (1 − x) m−k is the Bernstein polynomial. This estimator was investigated in the literatures [15][16][17][18] and, more recently, by [12,19,20].…”

Section: Introductionmentioning

confidence: 99%

Semi-Parametric Estimation Using Bernstein Polynomial and a Finite Gaussian Mixture Model

Helali

Masmoudi

Slaoui

2022

Entropy

Self Cite

View full text Add to dashboard Cite

The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact support. Among these methods, we mention Bernstein polynomials which leads to an improvement of edge properties for the density function estimator. In this paper, we set forward a shrinkage method using the Bernstein polynomial and a finite Gaussian mixture model to construct a semi-parametric density estimator, which improves the approximation at the edges. Some asymptotic properties of the proposed approach are investigated, such as its probability convergence and its asymptotic normality. In order to evaluate the performance of the proposed estimator, a simulation study and some real data sets were carried out.

show abstract