Published on:

29 November 2023

Primary Category:

Statistics Theory

Paper Authors:

Kensuke Aishima

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

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Extends prior analysis that only covered minimal norm TLS solutions

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Allows some rows of data matrices to be error-free

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Uses matrix perturbation theory and Rayleigh-Ritz projections

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Generalizes consistency proofs for standard unconstrained TLS

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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