Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models

Guan-Yu Chen; Dong-Yue Xie; Xi Yang

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arXiv · 2509.06856

Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models

Guan-Yu Chen·Dong-Yue Xie·Xi Yang

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Abstract

We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and Iterative-Sketching methods for the first time. By iteratively constructing and solving sketched least-squares (LS) subproblems with increasing sketch sizes to achieve better precisions, SLSE-FRS gradually refines the estimators of the true parameter vector, ultimately producing high-precision estimators. We analyze the convergence properties of SLSE-FRS, and provide its efficient implementation. Numerical experiments show that SLSE-FRS outperforms the state-of-the-art methods, namely the Preconditioned Conjugate Gradient (PCG) method, and the Iterative Double Sketching (IDS) method.

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BibTeX RIS

Guan-Yu Chen, Dong-Yue Xie, Xi Yang. 2025-09-08. Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models. https://arxiv.org/abs/2509.06856

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