| 李俞利,胡宏昌.序贯Lq似然比型检验*[J].数学年刊A辑,2023,44(4):363~382 |
| 序贯Lq似然比型检验* |
| Sequential Lq-Likelihood-Ratio-Type Test |
| Received:December 15, 2022 Revised:June 12, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0026 |
| 中文关键词: 序贯Lq似然比型检验, 基本恒等式, 势函数, 最优 q 值, 稳健性 |
| 英文关键词:Sequential Lq-likelihood-ratio-type test, Basic Identity, Power function, The optimal q value, Robustness |
| 基金项目:湖北省自然科学基金-黄石联合资助基金 (No.2022CFD042) |
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| 中文摘要: |
| 本文研究了序贯Lq似然比型检验(简写为SLqRT), 以及SLqRT的一些性质.基于其中一个性质--基本恒等式, 得到SLqRT的势函数和平均子样容量.为了节约成本, 通过最小化平均子样容量来选择合适的q值,从而进行指数分布的假设检验. 此外,给出了理论推导及两个模拟算例来说明SLqRT的稳健性,并计算了不同污染参数下粗差模型的序贯概率比检验(简写为SPRT)和SLqRT的平均子样容量.结果表明: 在平均子样容量下, SLqRT的效果优于SPRT. |
| 英文摘要: |
| In the paper, the authors investigate the sequential Lq-likelihood-ratio-type test(for short SLqRT), and some properties of the SLqRT. Based on one of these properties–the basic identity, the power function and the average sample size of the SLqRT are obtained.In order to save cost, they select the appropriate q value for the hypothesis test of the exponential distribution by minimizing the average sample size. In addition, they also give the theoretical derivation and two simulation examples to show the robustness of the SLqRT. Moreover, they calculate the average sample sizes of sequential probability ratio test(for short SPRT) and SLqRT under the gross error model with different contamination parameters. And the results shows that the SLqRT is better than the SPRT under the average sample size. |
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