# The maximum likelihood estimation for multivariate EIV model

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## Abstract

In this paper, a new method of parameter estimation for multivariate errors-in-variables (MEIV) model was proposed. The formulae of parameter solution for the MEIV model were deduced based on the principle of maximum likelihood estimation, and two iterative algorithms were presented. Since the iterative process is similar to the classical least square, both of the proposed algorithms are easy to program and understand. Finally, real and simulation datasets of affine coordinate transformation were employed to verify the applicability of the proposed algorithms. The results show that both of the proposed algorithms can achieve identical parameter estimators as those obtained by Lagrange algorithm and Newton algorithm. Additionally, the proposed Algorithm 2 can solve the MEIV model with higher convergence efficiency than Algorithm 1.

## Keywords

Total least squares Multivariate errors-in-variables model Parameter estimation Iterative algorithm## Notes

### Acknowledgements

This research was supported by the Natural Science Foundation of Hunan Province (No.2017JJ5035) and the Natural Science Foundation of Jiangsu Province (No. BK20180720).

### Compliance with ethical standards

### Conflicts of interest

The authors declare no conflict of interest.

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