Structural Risk Minimization Principle-Based EIV Model With Parameter Estimation Method

Regarding the EIV model,that is,both the explanatory variable and the explanatory variable have random errors.The weighted overall least squares(WTLS)method is an effective estimation method and can achieve higher precision.However,this method only considers the fitness of the model and ignores the complexity,which reduces its generalization ability.Based on the principle of structural risk minimization,this paper proposes the EIV model parameter ridge estimation method and LASSO estimation method.The main work is as follows:(1)Based on the principle of structural risk minimization,the EIV model parameter with ridge estimation(PRE)method is proposed,and the conditional equation satisfied by the optimal parameter estimation is derived using the lagrange multiplier method,and the numerical solution is given in iterative algorithm.To illustrate the effectiveness of the PRE method,this paper uses Monte Carlo method for numerical simulation and compares it with the least squares(LS)method,the ridge estimation(RE)method and the weighted total least squares(WTLS)method.The results show that the PRE method can significantly improve the precision and has the advantages of stronger generalization ability.(2)Based on the principle of structural risk minimization,the EIV model parameters with LASSO estimation(LE)method can achieve dimensionality reduction of high-dimensional data is proposed.Based on the mathematical derivation using lagrange multiplier method,the fast convergence iteration of its numerical solution is given algorithm.To illustrate the effectiveness of the LE method,this paper uses monte carlo method for numerical simulation and compares it with the WTLS and LS methods through empirical results.The results show that the LE method can significantly improve the prediction accuracy and has stronger generalization At the same time,it can achieve variable selection and achieve the purpose of dimensionality reduction of high-dimensional data.(3)Through empirical comparison between the two methods of PRE and LE,the conclusion is:from an economic perspective,the estimation results of the two methods are in line with actual economic significance;from the perspective of prediction accuracy and goodness of fit,LE is higher than PRE;from From the perspective of dimensionality reduction,LE is more effective than PRE.