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The problem of estimation of the integral of the squared derivative of a probability density $ f $ is considered using wavelet orthonormal bases. For $ f $ such that $ f^{(d)} $, the $ d $-th derivati...ve belongs to the Sobolev space $ H_2^s , s > 0 $, we obtain the precise asymptotic expression for the mean integrated squared error of the wavelet estimator.show more
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