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A new sequential signed-rank test for the one-sample location problem
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AI
DOI：10.1080/03610918.2025.2571976.png)
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Abstract
En 中文
We propose a new nonparametric sequential test for the one-sample location problem, specifically for the median of a symmetric continuous distribution, based on the signed-rank statistic. Approximate relationships between the stopping bounds of the test, and its size (alpha) and average sample number under the null hypothesis (ASN0) are derived by fitting regression models to simulated data. These models are reasonably accurate and facilitate the design of the test in practice. Alternatively, machine learning algorithms such as Random Forest and Gradient Boosting can precisely determine the stopping bounds using the simulated data. The performance of the proposed test is evaluated against existing nonparametric sequential tests, including the two-sided sequential sign test (TSST) and Miller's sequential signed-rank test (Miller's SSRT), using performance metrics such as power, ASN, and the power-to-ASN ratio (PAR). Extensive simulations demonstrate that the proposed test generally outperforms the TSST in terms of the PAR, in detecting a change of any size in the median. The proposed test is a generally preferable alternative to the TSST and a viable alternative to Miller's SSRT, particularly in scenarios where detecting small median changes with reasonably small ASN0 and small alpha is critical.
Keywords:
Machine learning algorithms
Nonparametric test
Power-to-ASN ratio
Test design
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C
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4.7K