2016/01/24 by Zhong Guan, Zhong Zhen Guan, Guan, Zhong · 1 citation
Engineering · Mathematics · #Applied mathematics #Bernstein polynomial #Combinatorics #Computer science #Control Systems and Identification #Deconvolution #Density estimation #Distribution (mathematics) #Estimator #Kernel (algebra) #Kernel density estimation #Mathematical analysis #Mathematics #Mean squared error #Polynomial #Probability density function #Rate of convergence #Sample size determination #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #stat.ME
paper · pdf · doi:10.48550/arxiv.1601.06432
published in arXiv (Cornell University) (Cornell University) · An error in the proof of Theorem 2
openalex publication_date 2016/01/24 · arxiv created 2018/01/26 · arxiv updated 2018/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial model, a finite mixture of specific beta distributions, is proposed. The change-point detection method is used to choose an optimal model degree. Based on a contaminated sample of size n, under an assumption which is satisfied, among others, by the generalized normal error distribution, the optimal rate of convergence of the mean integrated squared error is proved to be k-1O(n-1+1/klog3 n) if the underlying unknown density has continuous 2kth derivative with k>1. Simulation shows that small sample performance of our estimator is better than the deconvolution kernel density estimator. The proposed method is illustrated by a real data application.