Abstract: Consider the regression model Yi=g(ti)+ei for i=1,...,n. Here ,and H is a specified class of continuous functions from T to R. Based on a finite series expansion of g, an M-estimate 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 discussed. We also consider M-estimates for semiparametric regression models and show that they are consistent and asymptotically normal.
Key words and phrases: Asymptotic normality, M-estimation, nonparametotic regression model, semiparametric regression model, spline smoothing technique.