Simple kernel estimators for certain nonparametric deconvolution problems

A. J. van Es and A. R. Kok

Statistics & Probability Letters, 1998, vol. 39, issue 2, 151-160

Abstract: We consider deconvolution problems where the observations are equal in distribution to X = [lambda]1E1 + ... + [lambda]mEm + Y, or to X = [mu]1L1 + ... + [mu]mLm + Y. Here the random variables in the sums are independent, the Ei are exponentially distributed, the Li are Laplace distributed and Y has an unknown distribution F which we want to estimate. The constants [lambda]i and [mu]i are given. These problems include exponential, gamma and Laplace deconvolution. We derive inversion formulas, expressing F in terms of the distribution of the observations. Simple kernel estimators of F and its density f are then introduced by plugging in standard kernel estimators of the distribution of the observations. The pointwise asymptotic properties of the estimators are investigated.

Keywords: Deconvolution; Kernel; estimation (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (3)

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