Robustness of sign tests for testing hypotheses about order of autoregression

Observations of autoregression are contaminated by additive isolated outliers with an unknown random distribution. Intensity of the outliers $\gamma_n$ is $\min(1,n^{-1/2}\gamma)$, where $\gamma \geqq 0$ is unknown, and $n$ is the data size. Robustness of sign tests for hypotheses about order of autoregression is considered. The result is formulated in terms of equicontinuity of limiting power with respect to $\gamma$ at $\gamma=0$.