White heteroscedasticty testing after outlier removal

Given the effect that outliers can have on regression and specification testing, a vastly used robustification strategy by practitioners consists in: (i) starting the empirical analysis with an outlier detection procedure to deselect atypical data values; then (ii) continuing the analysis with the selected non-outlying observations. The repercussions of such robustifying procedure on the asymptotic properties of subsequent specification tests are, however, underexplored. We study the effects of such a strategy on the White test for heteroscedasticity. Using weighted and marked empirical processes of residuals theory, we show that the White test implemented after the outlier detection and removal is asymptotically chi-square if the underlying errors are symmetric. Under asymmetric errors, the standard chi-square distribution will not always be asymptotically valid. In a simulation study, we show that - depending on the type of data contamination - the standard White test can be either severely undersized or oversized, as well as have trivial power. The statistic applied after deselecting outliers has good finite sample properties under symmetry but can suffer from size distortions under asymmetric errors.