Sharp optimality and some effects of dominating bias in density deconvolution
نویسندگان
چکیده
We consider estimation of the common probability density f of i.i.d. random variables Xi that are observed with an additive i.i.d. noise. We assume that the unknown density f belongs to a class A of densities whose characteristic function is described by the exponent exp(−α|u|r) as |u| → ∞, where α > 0, r > 0. The noise density is supposed to be known and such that its characteristic function decays as exp(−β|u|s), as |u| → ∞, where β > 0, s > 0. Assuming that r < s, we suggest a kernel type estimator that is optimal in sharp asymptotical minimax sense on A simultaneously under the pointwise and the L2-risks. The variance of this estimator turns out to be asymptotically negligible w.r.t. its squared bias. For r < s/2 we construct a sharp adaptive estimator of f . We discuss some effects of dominating bias, such as superefficiency of minimax estimators. Mathematics Subject Classifications: 62G05, 62G20
منابع مشابه
Sharp optimality for density deconvolution with dominating bias
We consider estimation of the common probability density f of i.i.d. random variables Xi that are observed with an additive i.i.d. noise. We assume that the unknown density f belongs to a class A of densities whose characteristic function is described by the exponent exp(−α|u|r) as |u| → ∞, where α > 0, r > 0. The noise density is supposed to be known and such that its characteristic function d...
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