Testing threshold effect in single-index models

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.