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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 inferential procedures are, however, underexplored. We study the effects of such a strategy on testing for heteroscedasticity. Specifically, 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. In a simulation study, we show that-depending on the type of outliers-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. Given these results, we devise an empirical modeling strategy to guide practitioners whose preferred approach is to remove outliers from the sample.

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 inferential procedures are, however, underexplored. We study the effects of such a strategy on testing for heteroscedasticity. Specifically, 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. In a simulation study, we show that-depending on the type of outliers-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. Given these results, we devise an empirical modeling strategy to guide practitioners whose preferred approach is to remove outliers from the sample.

In this paper we provide considerable Monte Carlo evidence on the finite sample performance of several alternative forms of White's [1982] IM test. Using linear regression and probit models, we extend the range of previous analysis in a manner that reveals new patterns in the behavior of the asymptotic version of the IM test - particularly with respect to curse of dimensionality effects. We also explore the potential of parametric and nonparametric bootstrap methods for reducing the size bias that characterizes the asymptotic IM test. The nonparametric bootstrap is of particular interest because of the weak conditions it imposes, but the results of our Monte Carlo experiments suggest that this technique is not without limitations. The parametric bootstrap demonstrates good size and power in reasonably small samples, but requires assumptions that may be auxiliary from the standpoint of a QMLE. We observe that the effects of violating one of these auxiliary assumptions has a non-trivial impact on the size of IM tests that employ this technique.

In this paper we provide considerable Monte Carlo evidence on the finite sample performance of several alternative forms of White's [1982] IM test. Using linear regression and probit models, we extend the range of previous analysis in a manner that reveals new patterns in the behavior of the asymptotic version of the IM test - particularly with respect to curse of dimensionality effects. We also explore the potential of parametric and nonparametric bootstrap methods for reducing the size bias that characterizes the asymptotic IM test. The nonparametric bootstrap is of particular interest because of the weak conditions it imposes, but the results of our Monte Carlo experiments suggest that this technique is not without limitations. The parametric bootstrap demonstrates good size and power in reasonably small samples, but requires assumptions that may be auxiliary from the standpoint of a QMLE. We observe that the effects of violating one of these auxiliary assumptions has a non-trivial impact on the size of IM tests that employ this technique.