Anatolyev, Stanislav (2004) “Inference when a nuisance parameter is weakly identified under the null hypothesis”, Economics Letters, Vol. 84, No. 2, pp. 245–254
When a nuisance parameter is weakly identified under the null hypothesis, the usual asymptotic theory breaks down and standard tests may exhibit significant size distortions. We provide asymptotic approximations under a drifting parameter DGP for distributions of classical tests and of those designed for the case of complete non-identification. Simulations with a simple SETAR model show that the usual asymptotic theory does fail, although actual sizes of the classical Likelihood Ratio test display surprising robustness to the degree of identification.
Paper in RePEc:
Paper in accepted version:
Donald W.K. Andrews and Patrik Guggenberger (2010) "Asymptotic size and a problem with subsampling and with the m out of n bootstrap", Econometric Theory, Vol. 26, pp. 426-468.