Recovering a function f from its integrals over hyperplanes (or line integrals in the two-dimensional case), that is, recovering f from the Radon transform Rf of f, is a basic problem with important applications in medical imaging such as computerized tomography (CT). In the presence of...

We show that the method of Kipnis and Varadhan [Comm. Math. Phys. 104 (1986) 1-19] to construct a Martingale approximation to an additive functional of a stationary ergodic Markov process via the resolvent is universal in the sense that a martingale approximation exists if and only if the...

While optimal rates of convergence in L <Subscript>2</Subscript> for spectral regularization estimators in statistical inverse problems have been much studied, the pointwise asymptotics for these estimators have received very little consideration. Here, we briefly discuss asymptotic expressions for bias and variance...</subscript>

In this note we develop tests for checking the hypothesis whether a regression function, which is identified via instrumental variables, belongs to some parametric family of functions. We show that this testing problem can essentially be reduced to testing whether a regression function in an...

We study non-parametric tests for checking parametric hypotheses about a multivariate density f of independent identically distributed random vectors Z1,Z2,... which are observed under additional noise with density [psi]. The tests we propose are an extension of the test due to Bickel and...

A new method in two variations for the identification of most relevant covariates in linear models with homoscedastic errors is proposed. In contrast to many known selection criteria, the method is based on an interpretable scaled quantity. This quantity measures a maximal relative error one...