Orthognal Regression Analysis On EV Models

General regression models only consider the error of explanatory variables, and ignore the error of explanatory variables. However, in Practice, explanatory variables and explanatory variables are ususlly observed values with measurement error. This will cause bias estimates of parameters inevitably. EV models consider the error of explanatory variables and explanatory variables. This paper discussed in terms of orthogonal regression estimation of the EV models, made the following three main works.1. Because of the rotation invariance of the orthogonal distance of point to hyperplane, the whole sample points can be linear transformed and make that minimizing fuction of orthogonal least absolute deviation is differenctiable about parameters. According to the conditions of first derivative and second derivative of the differenctiable functions, hyperplane must pass through p+1 sample points in p dimensions linear models.2. This paper introduced smoothed method into orthogonal least absolute deviation, and proposed the method of smoothed orthogonal least absolute deviation estimation. Solve the calsulation problem of orthogonal least absolute estimation under the case of the large sample volume and high dimension3. This paper applied the smoothed orthogonal least absolute deviation to linear EV models and simple nonlinear EV models, and improved Newton iteration formula in the process of calculation, solve the nonconvergence issures of parameters in nonlinear EV models in a certain extent. By adding the abnormal points, verify the better stability of smoothed orthogonal least absolute estimation.