Statistica Sinica

Jiti Gao and Peide Shi

Abstract:Consider the regression modelY_{i}=g(t_{i})+e_{i}fori=1,...,n. Here ,andHis a specified class of continuous functions fromTtoR. Based on a finite series expansion ofg, anM-estimate ofgis constructed, and the asymptotic normality of the estimate is investigated. Meanwhile, a test statistic for testingH_{0}:g(.)=g_{0}(.) (a known function) is discussed. We also considerM-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.