Nonparametric Estimation In Nonlinear Models With Double Error Variables

Nonlinear models with double error variables have wide applications in the actual production and life. In the practice, we need to know the probability densitys of the errors in advance. In order to meet the requirement, we usually assume that the probability densitys of the errors belong to an known distrbution family. The fact is that this assumption is not consistent with the actual situation in many cases, and sometimes this assumption maybe get greater deviation.In this paper, we give the weighted local linear estimate of the regression function in the model firstly. Under certain conditions, we select the speed of convergence of the estimate. When we estimate the density of the error variable, for there are two error variables in the model, and an error is known to be normal distributed, we use the characteristic function to construct the deconvolution kernel estimate of the density of another variable which has the form of the kernel estimate. Under certain conditions, we also prove the convegence of the estimate.