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Biometrika 1988 75(4):639-650; doi:10.1093/biomet/75.4.639
© 1988 by Biometrika Trust
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Detecting dependencies in smooth regression models

MÜLLER HANS-GEORG and ULRICH STADTMÜLLER

Universität Erlangen-Nürnberg, Institut für medizinische Statistik 8520 Erlangen, Federal Republic of Germany
Universität Ulm Abteilung für Mathematik III, 7900 Ulm, Federal Republic of Germany

A class of simple estimators for the correlation of the errors in nonparametric regression models is proposed for the fixed design case. These estimators are based on squared differences of various spans of the data and are consistent so long as the regression function is Lipschitz continuous. The limiting distribution is established and applied to derive asymptotic ‘global’ and ‘local’ tests for different null hypotheses of uncorrelatedness. The finite sample behaviour of estimators and tests is investigated in a Monte Carlo study. A more general class of estimators using generalized difference schemes is also introduced.

Key Words: Correlation • m-dependence • Nonparametric regression • Residual analysis • Serial correlation


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