New second order approximation method for posterior precision evaluation of weighted total least squares estimates with analytical expression

Abstract

Several first order approximate methods to evaluate the posterior precision of weighted total least squares estimates have been developed but there is still some space for the methods of precision estimation. Therefore, a new second order approximate estimation method (SOA) is proposed which can consider the biases of the estimated parameters. The formulae of the new SOA are derived from the partial differential equation of objective function and the definition of variance covariance. And then, with the help of the second order Taylor expansion, the bias from the nonlinearity of EIV can be modified to improve the precision representation ability. Two simulated experiments are designed to verify the proposed SOA, and numerical results show that the proposed SOA is better and closer to the reference value than four selected competitors.

Keywords:

• Bias correction
• Errors in variables
• Posterior precision estimation
• Second order approximation
• Weighted total least squares

Additional information

Funding

The work described in this paper is supported by the Shanghai Municipal Natural Science Foundation (19ZR1459700).