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Mathematics Subject Classiication. 62G077 Secondary 62G20

1991
unpublished

Let a function f be observed with noise. In the present paper we concern the problem of nonparametric estimation of some non-smooth functionals of f , more precisely, L r-norm kfk r of f. Existing in the literature results on estimation of functionals deal mostly with two extreme cases: estimation of a smooth (diierentiable in L 2) functional or estimation of a singular functional like the value of f at a certain point or the maximum of f. In the rst case, the rate of estimation is typically n

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