This paper studies the wild bootstrap-based test proposed in Cameron et al. (2008). Existing analyses of its properties require that number of clusters is "large." In an asymptotic framework in which the number of clusters is "small," we provide conditions under which an unstudentized version of the test is valid. These conditions include homogeneity-like restrictions on the distribution of covariates. We further establish that a studentized version of the test may only over-reject the null hypothesis by a "small" amount that decreases exponentially with the number of clusters. We obtain qualitatively similar result for "score" bootstrap-based tests, which permit testing in nonlinear models.
Active Fault Diagnosis Based on Stochastic Tests
