Asymptotic normality for deconvolution kernel density estimators from random fields

2008/10/17 by Jiexiang Li, Li, Jiexiang · 3 citations
Environmental Science · Mathematics · #62G07 #62G20 (Primary) 62M40 (Secondary) #FOS: Mathematics #Soil Geostatistics and Mapping #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0810.3121

openalex publication_date 2008/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper discusses the estimation of a continuous density function of the target random field X_\bfi, \bfi∈ \mathbb Z^N which is contaminated by measurement errors. In particular, the observed random field Y_\bfi, \bfi∈ \mathbb Z^N is such that Y_\bfi=X_\bfi+ε_\bfi, where the random error ε_\bfi is from a known distribution and independent of the target random field. Compared to the existing results, the paper is improved in two directions. First, the random vectors in contrast to univariate random variables are investigated. Second, a random field with a certain spatial interactions instead of i. i. d. random variables is studied. Asymptotic normality of the proposed estimator is established under appropriate conditions.

Cited by

• Deconvolution in unlinked linear models
• Deconvolution of distribution functions without integral transforms
• Deconvolution of Arbitrary Distribution Functions and Densities

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