Pré-Publication, Document De Travail Année : 2026

Numerical Stability and Efficiency of Algorithms for Estimating the Asymptotic Variance of a Ratio Estimator

Résumé

We investigate several algorithms for estimating the asymptotic variance of a ratio estimator. The conventional ("standard") variance estimator can be prone to catastrophic cancellation-a numerical issue that arises when subtracting two nearly equal floating-point numbers, often leading to large relative errors. To mitigate this, we explore two alternative approaches: a two-pass algorithm and a one-pass method. Our analysis focuses on the numerical stability of the resulting estimators, showing that both the two-pass and one-pass approaches can yield more accurate results than the standard method. However, the two-pass technique requires storing the entire dataset, which may be impractical for large or streaming samples. In contrast, the one-pass method operates with constant memory. We illustrate the performance of these algorithms through numerical experiments on a simple example.

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hal-05596249 , version 1 (19-04-2026)

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  • HAL Id : hal-05596249 , version 1

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Marvin K Nakayama New, Bruno Tuffin. Numerical Stability and Efficiency of Algorithms for Estimating the Asymptotic Variance of a Ratio Estimator. 2026. ⟨hal-05596249⟩
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