Fast QR updating methods for statistical applications

TL;DR

This paper presents efficient algorithms for updating QR decompositions rapidly in statistical models, significantly reducing computational costs in dynamic data scenarios.

Contribution

It introduces novel R updating algorithms that enable fast, scalable QR decomposition updates for high-dimensional statistical applications.

Findings

Achieves substantial reduction in computational time

Maintains accuracy in dynamic data updates

Enhances feasibility of large-scale statistical analyses

Abstract

This paper introduces fast R updating algorithms specifically designed for statistical applications, including regression, filtering, and model selection, where data structures change frequently. Although traditional QR decomposition is essential for matrix operations, it becomes computationally intensive when dynamically updating the design matrix in statistical models. The proposed algorithms efficiently update the R matrix without the need for recalculation of Q, thereby significantly reducing computational costs in practical computational scenarios. The provision of scalable solutions for high-dimensional regression models is a key strength of these algorithms, enhancing the feasibility of large-scale statistical analyses and model selection in data-intensive fields. A thorough simulation study and the analysis of real-world data demonstrate that the methods achieve a substantial reduction in computational time without compromising accuracy. The discussion illustrates the benefits of these algorithms across a wide range of models and applications in statistics and machine learning.