Research On Semiparametric Measurement Error Model With Missing Value

The missing data and the existence of measurement errors in real life bring great challenges to statistical analysis.When there are both missing and measurement errors in the data,how to further mine the information of the data has important research significance.Partially linear model is a typical semi-parametric model,it combines the advantages of parametric model and non-parametric model,and it can also fit real data more flexibly,consequently it has a wide range of applications.Furthermore,compared with the classical least squares regression method,least absolute deviation regression(LAD)method is less susceptible to thick-tail data,which means that it is more robust than least squares regression method.Under the missing response variables,the robust estimator of partially linear measurement error model is studied.The main research content includes the following two aspects.First,combining orthogonal regression(OR)and least absolute deviation regression method,under the missing response,the estimation method of the parametric part and nonparametric function of the partially linear measurement error model is determined.Then,under certain regular conditions,the asymptotic normality of the parameter estimator and the convergence speed of the nonparametric function estimator are proved.Some numerical simulations and a real data analysis are used to explain the performance of the method.Second,instrumental variables(Ⅳ)is combined with least absolute deviation regression method,choosing the estimation method of the parametric part and non-parametric function of the partially linear measurement error model under the missing response variables.Under certain regular conditions,the asymptotic normality of the parameter estimator and the convergence speed of the non-parametric function estimator are proved.Explaining the performance of the method through some numerical simulations.