A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and only if the "trueʺ regression function is...

We propose and study a class of regression models, in which the mean function is specified parametrically as in the existing regression methods, but the residual distribution is modeled nonparametrically by a kernel estimator, without imposing any assumption on its distribution. This...

Quadratic loss is predominantly used in the literature as the performance measure for nonparametric density estimation, while nonparametric mixture models have been studied and estimated almost exclusively via the maximum likelihood approach. In this paper, we relate both for estimating a...

Smoothing methods for density estimators struggle when the shape of the reference density differs markedly from the actual density. We propose a bootstrap bandwidth selector where no reference distribution is used. It performs reliably in difficult cases and asymptotically outperforms well known...