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**1 - 2**of**2**### Adaptive empirical Bayesian smoothing splines. arXiv: 1411.6860 [math.ST

, 2014

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, 2015

"... Model (non-parametric regression) Consider n observations from the non-parametric regression model Yi = f(xi) + σi, i = 1,..., n. • The function f belongs to the Sobolev space Wβ(M), β ≥ 1/2. • The observation errors 1,..., n are i.i.d. standard Gaussian, and σ2> 0. • Parameters f, β, and σ2 are ..."

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Model (non-parametric regression) Consider n observations from the non-parametric regression model Yi = f(xi) + σi, i = 1,..., n. • The function f belongs to the Sobolev space Wβ(M), β ≥ 1/2. • The observation errors 1,..., n are i.i.d. standard Gaussian, and σ2> 0. • Parameters f, β, and σ2 are unknown and of interest. We work under the frequentist assumption: the data Y = (Y1,..., Yn) follow the model above for some ”true”parameters f and σ. 2 / 16 The estimators (smoothing splines) The minimiser of the penalised least squares criterium 1 n n∑ i=1 Yi − f(xi)