Abstract
This article gives sufficient conditions that guarantee the existence of minimizers of special classes of functions. Using these results, a certain dass of minimum distance (MD) estimators of the autoregressive parameters is shown to exist under the additive and innovative outliers; that is, autoregression (AO and IO) models. Through simulations, a certain subclass of MD estimators is shown to perform as good as or in some cases even better than other classical estimators like GM and functional least square estimators under the IO and AO models. Simulation results also show that MD estimators are robust against AO's.
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