Confidence bands for smoothness in nonparametric regression

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...

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...

Supplement to “Adaptive Confidence Bands for Nonparametric Regression Functions”

This supplement contains the proofs of Theorem 2, Propositions 2 and 3, Lemma 1 and Eq.(14). 7 Proof of Theorem 2 Rather than prove Theorem 2 directly it is convenient to first prove an analogue of the Theorem in the context of multivariate Normal random vectors. This is done in section 7.1. The proof of Theorem 2 is then given in section 7.2 7.1 Confidence Bound For Multivariate Normal Vectors...