A Short Information-Theoretic Analysis of Linear Auto-Regressive Learning
This provides a theoretical foundation for parameter estimation in linear auto-regressive models, but it is incremental as it offers an alternative information-theoretic proof rather than a new method.
The paper tackles the problem of proving consistency and non-asymptotic rates for the Gaussian maximum likelihood estimator in linear auto-regressive models, achieving nearly optimal rates without requiring stability assumptions for finite hypothesis classes.
In this note, we give a short information-theoretic proof of the consistency of the Gaussian maximum likelihood estimator in linear auto-regressive models. Our proof yields nearly optimal non-asymptotic rates for parameter recovery and works without any invocation of stability in the case of finite hypothesis classes.