Joint Hypothesis Testing from Heterogeneous Samples under Cross-dependence

Abstract

A testing principle is introduced that allows to combine evidence from $N$ potentially correlated samples. It builds on a (weighted) sum of entities from the individual samples, which is fed into a self-normalizing variance ratio type statistic. Due to self-normalization the (autoco)variances within each sample as well as the cross-covariances between the samples melt into one scaling parameter that cancels from the ratios asymptotically. Tests constructed from this principle are hence robust with respect to cross-dependence without having to estimate any nuisance parameters. The weighting and the entities from the individual samples depend on the testing problem at hand. Two cases are discussed in detail. The first one are tests of restrictions on a parameter vector (e. g. testing restrictions on expected values), while the second one focusses on time series: panel integration tests (unit root as well as stationarity tests). The validity of the asymptotic theory in finite samples is established by means of simulation evidence.