Application Of Empirical Likelihood Method In Nonlinear Models

In this paper,we mainly discuss the application of the empirical likelihood method in the ordinary nonlinear models and the nonlinear error-in-response models.In the ordinary nonlinear model Y=g(X,β)+e,we construct empirical log-likelihood ratio statistic for the unknown parameter.It is show that the proposed statistic have the asymptotic chi-square distribution,and the result can be used to construct the confidence regions ofβ.When there is error in observing response vari-able Y,without assuming any structure models between Y and surrogate variable(?),let Z=((?),X),u(z)= E[Y|Z=z],ε=e-(Y-u(Z)),the model can be equally changed to u(Z)= g(X,β)+ε,where the function u(.)generally is unknown.Using semipara-metric dimensional reduction and kernel regression technique,we give the estimation of u(z)with the help of validation data and construct the estimated empirical likeli-hood ratio statistic resp.adjusted empirical likelihood ratio statistic ofβ.It is show that they have the asymptotic weighted sum of chi-square variables distribution resp. have be asymptotic standar chi-square distribution,accordingly,confidence regions ofβcan be constructed.