M-TYPE SMOOTHING SPLINES IN NONPARAMETRIC AND SEMIPARAMETRIC REGRESSION MODELS

Abstract

Consider the regression model Yi = g(ti )+ ei for i =1 ,...,n .H ere −∞ <Y i,ei < ∞, ti ∈ T ⊂ R d , g ∈ H ,a ndH is a specified class of continuous functions from T to R. Based on a finite series expansion ˜ gn of g ,a nM-estimate ˆn of g is constructed, and the asymptotic normality of the estimate is investigated. Meanwhile, a test statistic for testing H0 : g(· )= g0(·) (a known function) is dis- cussed. We also consider M-estimates for semiparametric regression models and show that they are consistent and asymptotically normal.