Rates of convergence for constrained deconvolution problem

Details Rates of convergence for constrained deconvolution problem Rates of convergence for constrained deconvolution problem

2003-06-16

arxiv.org/abs/math/0306237v1

Mathematics

Statistics Theory

Scientific paper

Let $X$ and $Y$ be two independent identically distributed random variables with density $p(x)$ and $Z=\alpha X+\beta Y$ for some constants $\alpha>0$ and $\beta>0$. We consider the problem of estimating $p(x)$ by means of the samples from the distribution of $Z$. Non-parametric estimator based on the sync kernel is constructed and asymptotic behaviour of the corresponding mean integrated square error is investigated.

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