Parameter Estimation Of Spatial Autoregressive Models With Measurement Error

Spatial data with measurement error are common in real life.People can reduce the measurement error through various techniques.But sometimes the measurement error has reached a level that can not be ignored.On the other hand,because of the spatial dependence of spatial data,the assumption of independence between observations is not held.In this case,if we ignore the measurement error and the spatial dependences in the data,and use traditional analysis methods such as least squares methods to estimate parameters,the estimation results tend to be biased.Therefore,it is important to study the method of parameter estimation of spatial autoregressive models with measurement error.This paper mainly studied the parameter estimation problem of the spatial autoregressive models with measurement error in explanatory variables.Firstly,the corrected likelihood estimation was used to obtain the parameter estimation in the model,and its asymptotic property was proved.Finally,the results of corrected likelihood estimation and two-stage least squares estimation were compared in two cases with known and unknown measurement error variances.The simulation results showed that under the simulation conditions of this paper,both estimation methods were effective,and the estimation effect of corrected likelihood estimation was slightly better than that of two-stage least squares estimation.