On confidence bands in nonparametric density estimation and regression

Nonparametric confidence bands in deconvolution density estimation

Uniform confidence bands for densities f via nonparametric kernel estimates were first constructed by Bickel and Rosenblatt [Ann. Statist. 1, 1071–1095]. In this paper this is extended to confidence bands in the deconvolution problem g = f ∗ ψ for an ordinary smooth error density ψ. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distri...

Confidence Bands in Nonparametric Time Series Regression

We consider nonparametric estimation of mean regression and conditional variance (or volatility) functions in nonlinear stochastic regression models. Simultaneous confidence bands are constructed and the coverage probabilities are shown to be asymptotically correct. The imposed dependence structure allows applications in many linear and nonlinear auto-regressive processes. The results are appli...

Adjusted Confidence Bands in Nonparametric Regression

Bootstrap Confidence Bands in Nonparametric Regression

In the present paper we construct asymptotic conndence bands in non-parametric regression. Our assumptions admit unequal variances of the observations and nonuniform, possibly considerably clustered design. The conndence band is based on an undersmoothed local linear estimator, and an appropriate quantile is obtained via the wild bootstrap made popular by HH ardle and Mammen (1990). We derive c...

Adaptive Confidence Bands for Nonparametric Regression Functions.

A new formulation for the construction of adaptive confidence bands in non-parametric function estimation problems is proposed. Confidence bands are constructed which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are...