We study the problem of estimating conditional distribution functions from data containing additional errors. The only assumption on these errors is that a weighted sum of the absolute errors tends to zero with probability one for sample size tending to infinity. We prove sufficient conditions...

Verl.Beschr.: Der Band liefert eine umfassende Einführung in die Grundprinzipien der Statistik und die zugrundeliegende mathematische Theorie des Zufalls. Die Autoren verdeutlichen den Nutzen dieser Theorie anhand der Anwendungen und legen besonderen Wert auf die mathematisch exakte Einführung...

A simulation model with outcome Y=m(X) is considered, where X is an Rd-valued random variable and m:Rd→R is p-times continuously differentiable. It is shown that an importance sampling Robbins–Monro type quantile estimate achieves for 0p≤d the rate of convergence...

Given the values of a measurable function m:Rd→R at n arbitrarily chosen points in Rd the problem of estimating m on whole Rd is considered. Here the estimate has to be defined such that the L1 error of the estimate (with integration with respect to a fixed but unknown probability measure) is...