The relative efficiency of sequential tests
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910035829850112 |
|---|---|
| author | Doerks, Henri Ekström, Erik Wang, Yuqiong |
| author_facet | Doerks, Henri Ekström, Erik Wang, Yuqiong |
| contents | While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required to achieve a given power of the test -- but by how much? To address this question, we focus on the scenario of testing the unknown drift of a Brownian motion, comparing the Wald sequential probability ratio test with tests that use a pre-determined fixed sample size. We provide precise bounds on the average reduction in sample size needed to achieve a desired precision. Specifically, we demonstrate that for symmetric error bounds, the sequential test reduces the average sample size by at least 36\% and by at most 75\%. Moreover, the reduction in sample size increases monotonically with the power of the test, meaning that the relative advantage of using a sequential test over a fixed sample size test grows as higher power is required. We also study the relative efficiency in the case with asymmetric error bounds, and we provide a lower bound in terms of the symmetric case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00216 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The relative efficiency of sequential tests Doerks, Henri Ekström, Erik Wang, Yuqiong Statistics Theory Probability 62L10, 62L15, 60G40 While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required to achieve a given power of the test -- but by how much? To address this question, we focus on the scenario of testing the unknown drift of a Brownian motion, comparing the Wald sequential probability ratio test with tests that use a pre-determined fixed sample size. We provide precise bounds on the average reduction in sample size needed to achieve a desired precision. Specifically, we demonstrate that for symmetric error bounds, the sequential test reduces the average sample size by at least 36\% and by at most 75\%. Moreover, the reduction in sample size increases monotonically with the power of the test, meaning that the relative advantage of using a sequential test over a fixed sample size test grows as higher power is required. We also study the relative efficiency in the case with asymmetric error bounds, and we provide a lower bound in terms of the symmetric case. |
| title | The relative efficiency of sequential tests |
| topic | Statistics Theory Probability 62L10, 62L15, 60G40 |
| url | https://arxiv.org/abs/2603.00216 |