Robust GM-estimators and tests in autoregressive schemes with outliers

This report deals with the methods of construction of generalized M-estimators and tests for statistical hypotheses. For these procedures we explore the qualitative robustness property when data is contaminated by additive single outliers with intensity $O(n^{-1/2}).$ Particularly we consider the problem of robust GM-testing for the autoregression order. The qualitative robustness is formulated in terms of test power equicontinuity. Also the construction of the asymptotically optimal in maxmin sense GM-tests is considered.