Publication Date: August 2011
This paper provides a set of results that can be used to establish the asymptotic size and/or similarity in a uniform sense of conﬁdence sets and tests. The results are generic in that they can be applied to a broad range of problems. They are most useful in scenarios where the pointwise asymptotic distribution of a test statistic has a discontinuity in its limit distribution.
The results are illustrated in three examples. These are: (i) the conditional likelihood ratio test of Moreira (2003) for linear instrumental variables models with instruments that may be weak, extended to the case of heteroskedastic errors; (ii) the grid bootstrap conﬁdence interval of Hansen (1999) for the sum of the AR coeﬀicients in a k-th order autoregressive model with unknown innovation distribution, and (iii) the standard quasi-likelihood ratio test in a nonlinear regression model where identiﬁcation is lost when the coeﬀicient on the nonlinear regressor is zero.
Asymptotically similar, Asymptotic size, Autoregressive model, Conﬁdence interval, Nonlinear regression, Test, Weak instruments
JEL Classification Codes: C12, C18, C22, C26