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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