The asymptotics for the estimators in a semiparametric regression model under infinite <i>r</i> -th moments

In this paper, we investigate the parametric component and nonparametric component estimators in a semiparametric regression model based on independent errors with mean zero, which are stochastically dominated by the random variable ε and Hr(x)=E|ε|rI(|ε|≤x) is the slowly varying function at infinity. The weak consistencies for the estimators are established under infinite r-th (1<r<2) moments and other suitable conditions. The results obtained in the paper improve and generalize the existing ones of identically distributed random errors to the case of stochastically dominated random errors and the existing results under finite moments to the case of infinite moments. In addition, some simulation studies including numerical simulation and real data analysis are presented.