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Optimal Quantile Principle for Selecting Variable Bandwidth in Regression Estimators

In: Computing Science and Statistics

Author

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  • Andrzej S. Kozek

    (The University of Texas at El Paso, Department of Mathematical Sciences)

  • Eugene F. Schuster

    (The University of Texas at El Paso, Department of Mathematical Sciences)

Abstract

The optimal neighbor principle in data-driven selection of the variable window bandwidth in the Nadaraya-Watson regression estimators results in a lack of continuity of the bandwidth as a function of the conditional argument. This causes a lack of smoothness in the corresponding regression estimator which is frequently observed in samples of small or moderate size. A remedy, called the optimal quantile principle, is proposed and studied. We show that it is possible to modify the well-developed optimality theory used in choosing the smoothing parameter in Nadaraya-Watson kernel regression to give conditions under which corresponding optimality properties hold for the case of our p-th quantile estimator. Experience with computer simulations using a nonlinear regression package is reported.

Suggested Citation

  • Andrzej S. Kozek & Eugene F. Schuster, 1992. "Optimal Quantile Principle for Selecting Variable Bandwidth in Regression Estimators," Springer Books, in: Connie Page & Raoul LePage (ed.), Computing Science and Statistics, pages 401-405, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2856-1_63
    DOI: 10.1007/978-1-4612-2856-1_63
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