General Asymptotic Confidence Bands Based on Kernel-type Function Estimators

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We establish uniform and non-uniform asymptotic simultaneous confidence bands for functionals of the distribution based on kernel-type estimators, which include the Nadaraya–Watson kernel estimators of regression functions and the Akaike–Parzen–Rosenblatt kernel density estimators. Our theorems, based upon functional limit laws derived by modern empirical process theory, allow data-driven local bandwidths for these statistics.

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