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August 19, 2026Statistics

On the rate of Gaussian approximation for online linear regression problems

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Authors

MSM. SheshukovaADA. DurmusMKM. Khusainov

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Overview

Theoretical analysis demonstrates normal approximation convergence rates in online linear regression, indicating explicit error bounds scaling with problem dimension.

Key Points

  • Determine the convergence rate of Gaussian approximation for online linear regression under a constant stepsize regime.
  • Derived non-asymptotic error bounds for online linear regression using constant stepsize updates.
  • Evaluated the mathematical dependence of convergence rates on problem dimension d and properties of the design matrix.
  • Characterized explicit theoretical bounds relating Gaussian approximation rates directly to dimension d and design matrix structure.
  • Established a normal approximation rate of order log n / n for large sample sizes when total iterations n are fixed in advance.

Cite This Study

Sheshukova et al. (2026) studied this question.

synapsesocial.com/papers/6a85636403308d306e2d67c1https://doi.org/10.1080/02331888.2026.2697195
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