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...

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...

In this paper we propose a new nonparametric test for conditional heteroskedasticity based on a measure of nonparametric goodness-of-fit (R²) that is obtained from the local polynomial regression of the residuals from a parametric regression on some covariates. We show that after being...

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.