Abstract
Let ( X 1, Y 1),…, ( X n , Y n ) be i.i.d. rv's and let m( x) = E( Y| X = x) be the regression curve of Y on X. A M-smoother m n ( x) is a robust, nonlinear estimator of m( x), defined in analogy to robust M-estimators of location. In this paper the asymptotic maximal deviation sup 0 ≤ t ≤ 1 | m n ( t) − m( t)| is considered. The derived result allows the construction of a uniform confidence band for m( x).
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