Abstract
We consider the GARCH-type model S = σ2Z where σ2 and Z are independent random variables. We assume that the density of σ2 is unknown with support [0, 1] but differentiable whereas the density fS of S is bounded. We will also assume that the probability density function of the random variable Z is known and has the same distribution as the ν-fold product of independent random variables uniformly distributed on the interval [0, 1]. We want to estimate the derivative of the density of σ2 from n independent and identically distributed observations of S. We will construct adaptive and non adaptive wavelet estimators for the derivative of the density and obtain sharp upper bounds on their mean integrated squared errors.
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