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Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems

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Abstract

We propose two estimates of the mode of the probability density function for nonparametric deconvolution problems. In fact, we observe Y=X+[xi], where [xi] is a measurement error with a known distribution f[xi], and we are interesting by estimating the mode of fX the unknown probability density function of X, where Y1,...,Yn are n i.i.d given observations of Y. We study the asymptotic properties of these mode estimates and the asymptotic normality of the two mode estimates is also given.

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