Asymptotic normality for deconvolution kernel density estimators from random fields

The paper discusses the estimation of a continuous density function of the target random field Xi, i ∈ Z N which is contaminated by measurement errors. In particular, the observed random field Yi, i ∈ Z N is such that Yi = Xi + ǫi, where the random error ǫi 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. AMS 2000 subject classifications. Primary 62G07, 62G20; Secondary 62M40.