Rank Tests under Uncertainty: Regression and Local Heteroscedasticity

Data are often affected by unknown heteroscedasticity, which can stretch the conclusions. This is even more serious in regression models, when data cannot be visualized. We show that the rank tests for regression significance are resistant to some types of local heteroscedasticity in the symmetric situation, provided the basic density of errors is symmetric and the score-generating function of the rank test is skew-symmetric. The performance of tests is illustrated numerically.