A theory of testing under non-standard conditions is developed. By viewing the likelihood as a function of the unknown parameters, empirical process theory enables us to bound the asymptotic distribution of standardized likelihood ratio statistics, even when conventional regularity conditions...

A new asymptotic theory of regression is introduced for possibly nonstationary time series. The regressors are assumed to be generated by a linear process with martingale difference innovations. The conditional variances of these martingale differences are specified as autoregressive stochastic...

The authors study the asymptotic distribution of econometric tests involving nuisance parameters that are not identified under the null hypotheses. In general, the asymptotic distributions depend upon a large number of unknown parameters. The authors show that a transformation based upon a...