Statistical Inference For Varying Coefficient Partially Linear Models Under The Auxiliary Information

In the estimation of varying-coefficient partially linear model, it’s indispensable importance to improve the accuracy of model parameter estimation and model’s practical utility by using auxiliary information. This paper mainly studies restricted statistical inference problem of varying-coefficient partially linear models with error-prone linear covariates and auxiliary information. This paper firstly uses the r-order local polynomial regression techniques to estimate the error-prone linear covariates which has auxiliary information, Secondly, restricted estimation of parameters are given by using profile least square estimate-on method, And prove that the estimation meet the asymptotic normality properties, Again using Lagrange multiplier test method verified the rationality of restricted conditions, In the original hypothesis this paper shows that the test statistic asymptotic standard chi square distribution. Finally, through the numerical simulation this paper do a comparison of estimation whether or not parameters with restricted conditions, then verified the finite sample properties of the estimation and testing methods.This paper also studies the restricted estimation of varying coefficient partially linear model with missing response variables and error-prone linear covariates. For the missing data this paper use imputation estimation method filling the missing data, using the modified least square estimation to give the restricted parameter estimation, Using the profile Lagrange multiplier test method to test the restricted estimation. And prove that the estimation meet the asympto-tic normality properties, In the original hypothesis this paper shows that the test statistic asymptotic standard chi square distribution. Finally through numerical simulation testing restricted parameters estimation which with missing data and the efficiency of hypothesis testing.