Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein Polynomial

2016/01/24 by Zhong Zhen Guan, Guan, Zhong
Mathematics · Engineering · #Statistical Methods and Inference #Control Systems and Identification #Statistical Methods and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.1601.06432

Abstract

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.

Citations

• On the Convergence Properties of the EM Algorithm

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