Abstract: The sequence of dependent random variables has been widely studied by scholars since its emergence, and the regression model plays an important role in practical application. Studying the consistency of the estimation of lower semiparametric regression model under the NSD (negatively superadditive dependent) dependent random variables sequence not only expands the application of the properties of dependent random variables, but also enriches the estimation theory of semiparametric regression mode. In this paper, the consistency of the estimation of the lower semi parametric regression model of NSD random variable sequence is obtained by using the tail cut technique of random variables and the properties of NSD random variables.

Key words: NSD random variable sequence, semiparametric regression model, consistency, tail cutting technique