Sharp Optimality in Density Deconvolution with Dominating Bias. II

By Cristina Butucea, Alexandre B. Tsybakov. 2008

108 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/249851d8bce562d5c4e733dcf2cfdd975c3e0491

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

In Statistics and Probability

Citations in the corpus

Spectral estimation of the fractional order of a Lévy process (2010, unknown): “Q deﬁne χ2(P,Q)=: Z dP dQ −1 2 dQ, if P≪Q, +∞, otherwise. 30 D. BELOMESTNY The following proposition is the main tool for the proof of lower bounds in the estimation case and can be found in Butucea and Tsybakov (2004). Proposition A.1. Let PΘ := {Pθ :θ∈ Θ} be a family of models. Assume that the”
Bayesian inverse problems with non-conjugate priors (2012, methodology): “hat (2.3) is an equality (up to constants). Taking k n≃ nε2 gives the optimal result using this method, yielding rate ξ n≃ nαε2α+1. In the severely ill-posed setting of Condition (S) it is known (see [5] for the case of density deconvolution) that the bias strictly dominates the variance as long as ”
Adaptive estimation of linear functionals in the convolution model and applications (2009, unknown): “and we can check similarly to Butucea and Tsybakov [6] that for m solution of (38) this sequence is equivalent to φn,a,r when n→∞.”
Rates of convergence for nonparametric deconvolution (2006, methodology): “The pointwise mean squared error (denoted by MSE) and mean integrated squared error (denoted by MISE) are established in [ 2 ]:”
Nonparametric estimation of the characteristic triplet of a discretely observed Lévy process (2008, methodology): “ log(|φemp(t)|)1Bc nh . The latter can be shown by exactly the same arguments that were used in the proof of (15) in Lemma 5.1. Proof of Theorem 4.1. The proof makes use of some of the ideas found in [10, 19]. Consider two L´evy triplets T1 = (0,σ2,ρ1) and T2 = (0,σ2,ρ2), where ρi(x) = λfi(x),i= 1,2”
A ridge-parameter approach to deconvolution (2007, background): “bs phenomenon type in the ﬁnal estimator; the oscillations can usually only be removed by ﬁtting a taper to the integrand. An approach of this type has recently been discussed by Butucea and Tsybakov [3]. A particularly signiﬁcant diﬃculty with kernel methods arises when fft δ vanishes at one or mor”