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>

We relax the moment conditions from a result in almost sure limit theory for U-statistics due to Berkes and Csaki [(Stochastic Process. Appl. 94 (2001) 105)]. We extend this result to the case of convergence to stable laws and also prove a functional version.

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...

We investigate to what extent convergence in production levels per worker has been achieved in Germany since unification. To this end, we model the distribution of GDP per employee across German districts using two-component normal mixtures. While in the first year after unification, the...

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...