Perturbation-based null hypothesis tests with an application to Clayton models

Null hypothesis tests are popularly used when there is no appropriate alternative hypothesis available, especially in model assessment, where the assumed model is evaluated with no model being considered an alternative. Motivated by a test for Clayton models in multivariate survival analysis, we propose a perturbation-based method for null hypothesis testing that makes use of the resampling approach in Jin et al. (Jin et al., Biometrika; 2001; 88, 381-390) to estimate the variance-covariance matrix of an estimator to avoid intractable variance estimation. The proposed tests are straightforward and theoretically justified. We apply the proposed method to modify the tests in Shih (Shih, Biometrika; 1998; 85, 189-200) for the assessment of Clayton models. The proposed tests present satisfactory performance in simulation studies. A colon cancer dataset further illustrates the proposed tests.