Minimax quadratic estimation of a quadratic functional

A method for improving wavelet threshold denoising in laser-induced breakdown spectroscopy

“…In other words, for the Sh j (ε) calculation, we use a white noise with the same variance σ 2 to replace the white noise ε in the noisy LIBS signal. The estimation method about the variance σ 2 of the white noise ε is proposed by Donoho [45].…”

Adaptive estimation of a quadratic functional of a density by model selection

“…Donoho and Nussbaum [6] proposed an estimator of λ∈N * β 2 λ in the Gaussian sequence model, with the prior information that the sequence (β λ , λ ∈ N * ) belongs to some ellipsoïd.…”

Renormalizing Experiments for Nonlinear Functionals

“…This is another sense in which success of renormalization entails quasi-linearity. We know that already for global quadratic functionals, the diculty o f the full problem can fail to be equivalent to the diculty of the hardest two-point subproblem; see the discussion in [5]. Hence we expect that the renormalization approach of this paper fails in such cases.…”