Asymptotic normality for deconvolution kernel density estimators from random fields

Details Asymptotic normality for deconvolution kernel density estimators from random fields Asymptotic normality for deconvolution kernel density estimators from random fields

2008-10-17

arxiv.org/abs/0810.3121v1

Mathematics

Statistics Theory

Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics

Scientific paper

The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ is such that $Y_{\bf{i}}=X_{\bf{i}}+\epsilon_{\bf{i}}$, where the random error $\epsilon_{\bf{i}}$ 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.

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