Abstract: In earlier work we demonstrated that iterated numerical integration outperforms ”standard” multivariate integration techniques for various function classes with singularities inside the domain of integration. We focus on the accuracy requirements to be applied in different directions or combinations of directions of iterated integrals. The integrals are approximated numerically in an ...

We consider the problem of estimating a density fX using a sample Y1, . . . , Yn from fY = fX ? fε, where fε is an unknown density function. We assume that an additional sample ε1, . . . , εm from fε is given. Estimators of fX and its derivatives are constructed using nonparametric estimators of fY and fε and applying a spectral cut-off in the Fourier domain. In this paper the rate of convergen...

‎consider an estimation problem in a one-parameter non-regular distribution when both endpoints of the support depend on a single parameter‎. ‎in this paper‎, ‎we give sufficient conditions for a generalized bayes estimator of a parametric function to be admissible‎. ‎some examples are given‎. ‎