Bernstein Polynomial Model for Grouped Continuous Data

2015/06/21 by Zhong Zhen Guan, Guan, Zhong
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1506.06330

openalex publication_date 2015/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein polynomial, as the mixture proportions of beta distributions, can be estimated using an EM algorithm. The optimal degree of the Bernstein polynomial can be determined using a change-point estimation method. The rate of convergence of the proposed density estimate to the true density is proved to be almost parametric by an acceptance-rejection arguments used in Monte Carlo method. The proposed method is compared with some existing methods in a simulation study and is applied to a real dataset.

Citations

• Remarks on Some Nonparametric Estimates of a Density Function

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