Rates of convergence for constrained deconvolution problem
نویسنده
چکیده
Let Z1, ..., Zn be i.i.d observations, where Zi = Xi +Yi and Xi and Yi are independent random variables. Assume that the distribution of Y ’s is known. The ordinary deconvolution problem is the problem of estimating the destribution of a random variables Xi from the observations Zi. In some situations (for instance, in signal processing) we don’t know the distribution of Yi but rather can assume that Xi and Yi belong to the same class of distributions (constrained deconvolution). For example, Xi and Yi may be of the same multiplicative type (see Belomestny (2002,2003)), that is
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