Theory and Method of Hypothetical Test for Nonparameters in Linear Semiparametric Model

The linear semiparametric regression model L=BX+s+△ is a combine of classical linear model with nonparametric regression model. Based on the basic theory of the penalized least squares for the semiparametric mode，this paper presents a detailed discussion on the theory and method of hypothetical test for nonparameters in the linear semiparametric model and the hypothetical test statictics are derived and its distribution are proved. Finally the validity of the proposed theory and method of the hypothetical test for nonparameter is confimed by simulated experiment.