We establish the asymptotic theory of least absolute deviation (LAD) estimators for AR(1) processes with autoregressive parameter satisfying $n(\rho_n-1)\to\gamma$ for some fixed $\gamma$ as $n\to\infty$, which is parallel to the results of ordinary least squares (OLS) estimators developed by Andrews and Guggenberger (Journal of Time Series Analysis, 29 (2008), 203-212) in the case $\gamma=0$ or Chan and Wei (Annals of Statistics}, 15 (1987), 1050-1063) in the case $\gamma\ne0$. We also provide the stochastic integral representation of the limit distribution for the estimator in the second case and discuss the connection with the existing results. Simulation experiments are conducted to confirm some of the theoretical results and to demonstrate the robustness of the LAD estimators. This is a joint work with Ma Nannan and Sang Hailin.

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