Abstract of On adaptation to sparse design in bivariate Local linear regression

Research Report SRR96-007

On adaptation to sparse design in bivariate Local linear regression

Peter Hall, Burkhardt Seifert and Berwin A. Turlach

Abstract: Local linear smoothing enjoys several excellent theoretical and numerical properties, and in a range of applications is the method most frequently chosen for fitting curves to noisy data. Nevertheless, it suffers numerical problems in places where the distribution of design points (often called predictors, or explanatory variables) is sparse. In the case of univariate design, several remedies have been proposed for overcoming this problem, of which one involves adding additional ``pseudo'' design points in places where the original design points were too widely separated. This approach is particularly well suited to treating sparse bivariate design problems, and in fact attractive, elegant geometric analogues of univariate imputation and interpolation rules are appropriate for that case. In the present paper we introduce and develop pseudo data rules for bivariate design, and apply them to real data.

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