WIAS Preprint No. 61, (1993)

Automatic bandwidth choice and confidence intervals in nonparametric regression.


  • Neumann, Michael H.

2010 Mathematics Subject Classification

  • 62G15 62G07 62G20


  • Nonparametric regression, bandwidth choice, confidence intervals, Edgeworth expansions




In the present paper we combine the issues of bandwidth choice and construction of confidence intervals in nonparametric regression. We modify the √n-consistent bandwidth selector of Härdle, Hall and Marron (1991) such that it is appropriate for heteroscedastic data and show how one can adapt the bandwidth g of the pilot estimator m̂g in a reasonable data-dependent way. Then we compare the coverage accuracy of classical confidence intervals based on kernel estimators with data-driven bandwidths. We propose a method to put undersmoothing with a data-driven bandwidth into practice and show that this procedure outperforms explicit bias correction.

Appeared in

  • Ann. Statist., 23 (1996), pp. 1937--1959

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