We study the problem of identifying a forecaster’s loss function from observations on forecasts, realizations, and the forecaster’s information set. Essentially different loss functions can lead to the same forecasts in all situations, though within the class of all continuous loss...

Building on work of McLeish, we present a number of invariance principles for doubly indexed arrays of stochastic processes which may exhibit considerable dependence, heterogeneity, and/or trending moments. In particular, we consider possibly time-varying functions of infinite histories of...

We consider two tests of structural change for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and...

We present a general theory of consistent estimation for possibly misspecified parametric models based on recent results of Domowitz and White. This theory extends the unification of Burguete, Gallant, and Souza by allowing for heterogeneous, time-dependent data and dynamic models. The theory is...

This note demonstrates that the conditions of Kotlarski’s (1967, <italic>Pacific Journal of Mathematics</italic> 20(1), 69–76) lemma can be substantially relaxed. In particular, the condition that the characteristic functions of <italic>M</italic>, <italic>U</italic> ₁, and <italic>U</italic> ₂ are nonvanishing can be replaced with much weaker conditions:...

We analyze fast procedures for conducting Monte Carlo experiments involving bootstrap estimators, providing formal results establishing the properties of these methods under general conditions.

We give a straightforward condition sufficient for determining the minimum asymptotic variance estimator in certain classes of estimators relevant to econometrics. These classes are relatively broad, as they include extremum estimation with smooth or nonsmooth objective functions; also, the rate...