The paper discusses asymptotic properties of penalized spline smoothing if the spline basis increases with the sample size. The proof is provided in a generalized smoothing model allowing for non-normal responses. The results are extended in two ways. First, assuming the spline coefficients to...

type="main" xml:id="rssb12047-abs-0001" <title type="main">Summary</title> <p>We introduce a new estimator, the simultaneous multiscale change point estimator SMUCE, for the change point problem in exponential family regression. An unknown step function is estimated by minimizing the number of change points over the...</p>

We consider the problem of estimating the noise variance in homoscedastic nonparametric regression models. For low dimensional covariates "t"  is an element of  <openface>R</openface>-super-"d", "d"&equals;1, 2, difference-based estimators have been investigated in a series of papers. For a given length of such an...

Uniform confidence bands for densities "f" via non-parametric kernel estimates were first constructed by Bickel and Rosenblatt. In this paper this is extended to confidence bands in the deconvolution problem "g"&equals;"f"*"ψ" for an ordinary smooth error density "ψ". Under certain regularity...

We propose two test statistics for use in inverse regression problems "Y"&equals;"K""&thgr;"&plus;"&epsiv;", where "K" is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations "Y" for the function "&thgr;" are available. Both test statistics have a counterpart in classical...