This paper studies the supremum-type score test for the single-index model against a threshold single-index model. It is shown that the test weakly converges a maxima of a Gaussian process under the null hypothesis. The bootstrap method is used to tackle the bias problem and provide the $p$-values of our test statistic. Simulations are carried out to assess the performance of our procedure and real data examples are given for its illustration.

中文翻译：

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在单指数模型中测试阈值效应

本文研究了单指标模型与阈值单指标模型的最高类型得分检验。结果表明，该检验在原假设下弱收敛高斯过程的最大值。bootstrap 方法用于解决偏差问题并提供我们的测试统计量的 $p$-values。进行了模拟以评估我们程序的性能，并给出了真实数据示例以进行说明。