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Strong consistency of rank-constrained total least squares regression

Paper Authors:

Kensuke Aishima

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Key Details

Proves strong consistency for solutions to rank-constrained total least squares (TLS) regression

Extends prior analysis that only covered minimal norm TLS solutions

Allows some rows of data matrices to be error-free

Uses matrix perturbation theory and Rayleigh-Ritz projections

Generalizes consistency proofs for standard unconstrained TLS

AI generated summary

Strong consistency of rank-constrained total least squares regression

This paper proves that a variant of total least squares regression with rank constraints yields estimators that converge to the true parameter values, even when the explanatory variables contain errors. This establishes asymptotic consistency for a broader set of solutions beyond just the minimal norm solution typically analyzed. The proof relies on matrix perturbation theory and properties of orthogonal projections derived from the Rayleigh-Ritz procedure.

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