The robust sign test for hypothesis about a unit root of autoregression

The observations of $AR(1)$ autoregression contain gross errors (contaminations). The distribution of these contaminations is unknown and arbitrary. We test the hypothesis about the unit root of the autoregression. The special sign test is suggested as an alternative to least squares test (which can not be used in such situation). The qualitative robustness of this test in terms of power equicontinuity is obtained.