Simulation-Extrapolation Estimation For Multiplicative Regression Model With Measurement Error

The multiplicative model is simple in form and has a good interpretation for the positive response variables.It is widely used in the fields of economy,finance,biomedicine and sociology.However,in some practical problems,the established multiplicative model may with measurement error for various reasons.At this time,the conventional estimation methods are no longer applicable,and new effective estimation methods need to be developed.This paper focuses on the estimation of constant coefficient multiplicative model and varying coefficient multiplicative model with measurement error.For the constant coefficient multiplicative model with the covariates being measured with additive error,surpose that the measurement error follows a normal distribution,we develop a simulation-extrapolation estimation method for unknown parameters based on the least product relative error criterion.Under certain conditions,the large sample properties of the given estimates are proved,including consistency and asymptotic normality.In addition,the performance of the proposed method is further examined by a large number of numerical simulations.For the varying coefficient multiplicative model with the covariates being measured with additive error,surpose that the measurement error follows a normal distribution,we develop a simulation-extrapolation estimation method for unknown coefficient function based on the local least product relative error criterion.Under weaker assumptions,the large sample properties of the obatined estimates are proved,including consistency and asymptotic normality.In the same way,the effectiveness of the proposed method is further verified by a large number of numerical simulations.