Abstract

A linear multivariate measurement error model AX=B is considered. The errors in are row-wise finite dependent, and within each row, the errors may be correlated. Some of the columns may be observed without errors, and in addition the error covariance matrix may differ from row to row. The columns of the error matrix are united into two uncorrelated blocks, and in each block, the total covariance structure is supposed to be known up to a corresponding scalar factor. Moreover the row data are clustered into two groups, according to the behavior of the rows of true A matrix. The change point is unknown and estimated in the paper. After that, based on the method of corrected objective function, strongly consistent estimators of the scalar factors and X are constructed, as the numbers of rows in the clusters tend to infinity. Since Toeplitz/Hankel structure is allowed, the results are applicable to system identification, with a change point in the input data.

Keywords: Linear errors-in-variables model; Corrected objective function; Clustering; Dynamic errors-in-variables model; Consistent estimator

Mathematical subject codes: 65F20; 93E12; 62H30; 62J05; 62H12; 62F12; 65P99

Article Outline

1. Introduction

2. General model without clustering

2.1. General assumptions

2.2. Derivation of the score function

2.3. Constructing the cost function under unknown

3. Model with two clusters

4. Estimation of the change point

5. Estimation of two scale factors

6. Final estimator of X

7. Simulation example

8. Conclusions

Acknowledgements

Appendix A. Proof of Theorem 4.1

Appendix B. Proof of Theorem 5.1

B.1. Behavior of Q_c(λ⁰)

B.2. is eventually bounded

B.3. Consistency

Appendix C. Proof of Theorem 6.1

References