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The Almon technique is a widely used estimation procedure for the distributed lag model (DLM) to encounter the problems associated with direct application of the ordinary least squares method to this model. The Almon estimator may be sensitive to outliers in the  y -direction. This study is aimed to propose a robust estimator for parameter vector of the DLM when data set is contaminated with outliers. Moreover, this study proposes the robust  t -tests and confidence intervals for the lag coefficients. Performance of our proposed estimator is evaluated through the Monte Carlo simulations by comparing the estimated mean squared error while the performance of  t -tests and confidence intervals is evaluated using the null rejection rates and coverage, respectively. The simulation results reveal an attractive performance of the proposed methods in the presence of outliers in the  y -direction.

The Almon M-estimator for the distributed lag model in the presence of outliers