We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series....

This paper presents an alternative method to derive the limiting distribution of residual-based statistics. Our method does not impose an explicit assumption of (asymptotic) smoothness of the statistic of interest with respect to the model's parameters. and, thus, is especially useful in cases...

We propose a class of simple rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which needs not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite sample size, is...

The standard efficient testing procedures in the Generalized Inverse Gaussian (GIG) family (also known as Halphen Type A family) are likelihood ratio tests, and hence rely on Maximum Likelihood (ML) estimation of the three parameters of the GIG. The particular form of GIG densities, involving...