Despite an abundance of semiparametric estimators of the transformation model, no procedure has been proposed yet to test the hypothesis that the transformation function belongs to a finite-dimensional parametric family against a nonparametric alternative. In this article, we introduce a bootstrap test based on integrated squared distance between a nonparametric estimator and a parametric null. As a special case, our procedure can be used to test the parametric specification of the integrated baseline hazard in a semiparametric mixed proportional hazard model. We investigate the finite sample performance of our test in a Monte Carlo study. Finally, we apply the proposed test to Kennan’s strike durations data.

中文翻译：

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测试参数转换模型与非参数替代模型

尽管变换模型有大量的半参数估计量，但尚未提出任何程序来检验变换函数属于有限维参数族的假设，而不是非参数替代方案。在本文中，我们介绍了一种基于非参数估计器和参数空值之间的积分平方距离的引导测试。作为一种特殊情况，我们的程序可用于在半参数混合比例风险模型中测试综合基线风险的参数规范。我们在蒙特卡洛研究中调查了我们测试的有限样本性能。最后，我们将建议的测试应用于凯南的罢工持续时间数据。