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Research Report SRR00-003
Thresholding and oracle inequalities for weighted
\chi2
Iain Johnstone
Abstract:
Given data from a spherical Gaussian distribution with
unknown mean vector \theta, estimates of quadratic functionals
$\rho_\alpha = \sum \alpha_k \theta_k^2$ are constructed by
thresholding. Mean squared error bounds are derived via a
comparison with those already available for a suitable noncentral
$\chi^2$ variate. By way of illustration, the resulting oracle
inequalities are used to yield an optimal rate adaptivity result
for estimation of $\int (D^l f)^2$ in the white noise model of
nonparametric function estimation.
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