1. Hampel's three-part M estimators have Ψ functions which are odd functions and defined for any x by:
This function is plotted in the following figure for a=1.645, b=3 and r=6.5.
2. Tukey's biweight or bisquare M estimators have Ψ functions for any positive k, which defined by:
This function is plotted in the following figure for k=5.
3. Andrew's sine wave M estimator has the following Ψ function:
This function is plotted in the following figure.
Read more about this topic: Redescending M-estimator
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