On nonparametric confidence set estimation
نویسندگان
چکیده
The problem of adaptive estimation of regression function from noisy observations is considered in the paper. We provide an adaptive confidence set B̂N of level 1− α, 0 < α < 1, for the unknown function f . Here B̂N is a L2-ball of (random) diameter τ̂N , centered at the wavelet adaptive estimate f̂N . We show that if it is known a priori that f belongs to a Besov functional class F∗, then the proposed confidence ball cannot be improved in the minimax sense.
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