Nonparametric density estimation from observations with multiplicative\n measurement errors

2017/09/02 by Denis Belomestny, Alexander Goldenshluger, Belomestny, Denis +1 · 2 citations
Mathematics · Medicine · #60G05 #60G20 #FOS: Computer and information sciences #Liver Disease Diagnosis and Treatment #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1709.00629

openalex publication_date 2017/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the problem of pointwise density estimation from\nobservations with multiplicative measurement errors. We elucidate the main\nfeature of this problem: the influence of the estimation point on the\nestimation accuracy. In particular, we show that, depending on whether this\npoint is separated away from zero or not, there are two different regimes in\nterms of the rates of convergence of the minimax risk. In both regimes we\ndevelop kernel--type density estimators and prove upper bounds on their maximal\nrisk over suitable nonparametric classes of densities. We show that the\nproposed estimators are rate--optimal by establishing matching lower bounds on\nthe minimax risk. Finally we test our estimation procedures on simulated data.\n

Cited by

• Goodness-of-fit testing from observations with multiplicative measurement error
• Deconvolution of arbitrary distribution functions and densities

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