Cristina Butucea

Adaptivity in convolution models with partially known noise distribution

We consider a semiparametric convolution model. We observe random variables having a distribution given by the convolution of some unknown density f and some partially known noise density g. In this work, g is assumed exponentially smooth with stable law having unknown self- similarity index s. In order to ensure identifiability of the model, we re- strict our attention to polynomially smooth, Sobolev-type densities f, with smoothness parameter �. In this context, we first provide a consistent esti- mation procedure for s. This estimator is then plugged-into three different procedures: estimation of the unknown densityf, of the functional R f 2 and goodness-of-fit test of the hypothesis H0 : f = f0, where the alternative H1 is expressed with respect to L2-norm (i.e. has the form 2

Adaptive goodness-of-fit testing from indirect observations

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density

Maximum entropy copula with given diagonal section

f

Sharp minimax tests for large Toeplitz covariance matrices with repeated observations

and some known noise density

Optimal exponential bounds for aggregation of estimators for the Kullback-Leibler loss

g

New M-estimators in semi-parametric regression with errors in variables

. We assume that

Maximum entropy distribution of order statistics with given marginals

g

Corrigendum: Spectral thresholding quantum tomography for low rank states (2015 New J. Phys. 17 113050)

is polynomially smooth. We provide goodness-of-fit testing procedures for the test

Sharp detection of smooth signals in a high-dimensional sparse matrix with indirect observations

H_0:f=f_0

Variable selection with Hamming loss

, where the alternative