On confidence bands for multivariate nonparametric regression
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Date
2014-01-14
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Abstract
In a multivariate nonparametric regression problem with fixed, deterministic design asymptotic,
uniform confidence bands for the regression function are constructed. The construction of the bands
is based on the asymptotic distribution of the maximal deviation between a suitable nonparametric
estimator and the true regression function which is derived by multivariate strong approximation
methods and a limit theorem for the supremum of a stationary Gaussian field over an increasing
system of sets. The results are derived for a general class of estimators which includes local polynomial
estimators as a special case. The finite sample properties of the proposed asymptotic bands are
investigated by means of a small simulation study.
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Keywords
confidence bands, uniform convergence, nonparametric regression, multivariate regression, rates of convergence