Deconvolving a Density from Partially Contaminated Observations

C. H. Hesse

Journal of Multivariate Analysis, 1995, vol. 55, issue 2, 246-260

Abstract: We consider the problem of estimating a continuous bounded probability density function when independent data X1, ..., Xn from the density are partially contaminated by measurement error. In particular, the observations Y1, ..., Yn are such that P(Yj = Xj) = p and P(Yj = Xj + [epsilon]j) = 1 - p, where the errors [epsilon]j are independent (of each other and of the Xj) and identically distributed from a known distribution. When p = 0 it is well known that deconvolution via kernel density estimators suffers from notoriously slow rates of convergence. For normally distributed [epsilon]j the best possible rates are of logarithmic order pointwise and in mean square error. In this paper we demonstrate that for merely partially(0

Date: 1995
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