Least-correlation estimates for errors-in-variables models. (English) Zbl 1138.62012
Summary: This paper introduces an estimator for errors-in-variables models in which all measurements are corrupted by noise. A necessary and sufficient condition minimizing a criterion, defined by squaring the empirical correlation of residuals, yields a new identification procedure that we call least-correlation estimator. The method of least correlation is a generalization of least-squares since the least-correlation specializes to least-squares when the correlation lag is zero. The least-correlation estimator has the ability to estimate true parameters consistently from noisy input-output measurements as the number of samples increases. Monte Carlo simulations also support the consistency numerically. We discuss the geometric property of the least-correlation estimate and, moreover, show that the estimate is not an orthogonal projection but an oblique projection. Finally, recursive realizations of the procedure in continuous-time as well as in discrete-time are mentioned with a numerical demonstration.
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