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...

In practical applications, when testing parametric restrictions for hidden Markov models (HMMs), one frequently encounters non-standard situations such as testing for zero entries in the transition matrix, one-sided tests for the parameters of the transition matrix or for the components of the...

We present a new approach to handle dependencies within the general framework of case-control designs, illustrating our approach by a particular application from the field of genetic epidemiology. The method is derived for parent-offspring trios, which will later be relaxed to more general...

In this paper we are concerned with analyzing the behavior of a semiparametric estimator which corrects for endogeneity in a nonparametric regression by assuming mean independence of residuals from instruments only. Because it is common in many applications, we focus on the case where endogenous...