To obtain consistency results for nonparametric estimators based on stochastic processes relevant in econometrics, we introduce the notions of Hilbert space-valued <italic>L</italic> mixingales and near-epoch dependent arrays, and we prove weak and strong laws of large numbers by using a new exponential...

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, <italic>f</italic>(<italic>y</italic>|<italic>x</italic>,<italic>z</italic>) and <italic>f</italic>(<italic>y</italic>|<italic>x</italic>), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value...

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...