Let f(y|x,z) (resp. f(y|x) be the conditional density of Y given (X,Z) (resp. X). We construct a class of `smoothed` empirical likelihood-based tests for the conditional independence hypothesis: Pr[f(Y|X,Z)=f(Y|X)]=1. We show that the test statistics are asymptotically normal under the null...

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 construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother...

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...