Thresholding for weighted χ
نویسنده
چکیده
Given data from a spherical Gaussian distribution with unknown mean vector θ, estimates of quadratic functionals are constructed by thresholding. Mean squared error bounds are derived via a comparison with those already available for a suitable noncentral χ variate. By way of illustration, the resulting inequalities are used to yield an optimal rate adaptivity result for estimation of integrated squared derivatives in the white noise model of nonparametric function estimation.
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