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Research Report SRR00-004
Chi-square oracle inequalities
Iain M. Johnstone
Abstract:
We study soft threshold estimates of the non-centrality
parameter \xi of a non-central \chid2(\xi)
distribution, of
interest, for example, in estimation of the squared length of the
mean of a Gaussian vector. Mean squared error and oracle bounds,
both upper and lower, are derived for all degrees of freedom
d. These bounds are remarkably similar to those in the limiting
Gaussian shift case. In nonparametric estimation of \int
f2, a
dyadic block implementation of these ideas leads to an alternate
proof of the optimal adaptivity result of Efromovich and Low.
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