Robust inference under heterogeneity, dependence, crises, structural breaks, outliers, and heavy-tailedness using conservativeness of test statistics

We consider general approaches to robust inference about scalar parameters of interest when the data is potentially heterogeneous and correlated in a largely unknown way, as is typically the case in finance and economics. The approaches are based on small sample conservativeness properties of the standard one-sample t-statistic established by Bakirov and Szekely (2005) and their analogues for the two-sample t-statistic for testing equality of means. These properties show that, for commonly used significance levels, the one-sample and two-sample t-tests remain conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference in the following simple way: partition the data into some number of groups, estimate the model for each group, and conduct standard one-sample or two-sample t-test with the resulting parameter estimators of interest. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data, and in inference on treatment effects, structural breaks, crises and heavy-tailed models.