U-STATISTICS IN GENERAL REGRESSION MODEL

In this paper, the estimation of the direction of the regression coefficient of general regression model is considered. According to the definition of general regression model, the conditional distribution of the outcome variable Y depends on X only through a linear combination β’X, where β is the regression coefficient vector of the model. General regression model is a generalization of linear model. In this paper, a series of U-statistics, which is to be the estimator of the direction of vector β, is constructed, and the consistency, asymptotic normality of the series are obtained.