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This article studies the weak convergence and associated Central LimitTheorem for blurring and nonblurring processes. Then, they are applied to theestimation of location parameter. Simulation studies show that the locationestimation based on the convergence point of blurring process is more robustand often more efficient than that of nonblurring process.

On the Weak Convergence and Central Limit Theorem of Blurring and Nonblurring Processes with Application to Robust Location Estimation