Jackknife resample method for precision estimation of weighted total least squares

Abstract

Few studies have been conducted on the precision estimation of weighted total least squares (WTLS) by using the approximate function probability distribution method. And the existing Monte Carlo method needs to simulate a lot, the amount of calculation is large and the results obtained are uncertain. In order to further improve the total least squares precision estimation theory, this paper introduces the Jackknife method into Geomatics data processing. Combining the Jackknife method and WTLS method, the delete-1 Jackknife method and delete-d Jackknife method are proposed. The biases and standard deviations or covariance of parameter estimations are calculated by these proposed methods. And the specific steps of the precision estimation of these two methods are given. Applying these methods to the linear regression model and the coordinate transformation model, and comparing with the approximate function method and the Monte Carlo method, we can see that the Jackknife methods for precision estimation can obtain more stable and reasonable precision results and are very adaptive. In order to get more reasonable precision results, the Jackknife method does spend much more time over total least squares when the amount of the observed data is large. But compared with Monte Carlo method, it can reduce the amount of calculation and improve the computational efficiency. The method in this paper could provide an idea for further study on the precision estimation for total least squares.

Keywords:

• Total least squares
• Precision estimation
• Delete-1 Jackknife method
• Delete-d Jackknife method
• Approximate function

Acknowledgments

The authors are grateful to Prof. N. Balakrishnan and all the anonymous reviewers for their valuable comments, which improve the quality of this paper.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (No. 41874001 and No. 41664001), Support Program for Outstanding Youth Talents in Jiangxi Province (No. 20162BCB23050) and National Key Research and Development Program (No. 2016YFB0501405). Innovation Fund Designated for Graduate Students of ECUT (DHYC-201809).