how to set parameter for robust regression?

Question

I am using the rlm R package and experimenting with robust regression using the Huber function. Here is my code:

myfit= rlm(formula = depvar ~ indep1+indep2, init="ls",data = my_input_data,psi =psi.huber, k=0.99,method = "M", maxit=200) 

k is the tuning parameter for the Huber function ( psi.huber ), which I set to 0.99 in my code above.

However, the default specified in the rlm R documentation is k = 1.345 .

I would appreciate any insights if it is commonly acceptable in statistics to change this tuning parameter. And is there any way to automatically determine this parameter through some optimization?

Answer 1

I think this might give you some pointers how to interpret the value of k : http://www.iwaenc.org/proceedings/1997/nsip97/pdf/scan/ns970534.pdf k is a borderline value of central Gaussian part of the distribution. Depending on the data, you might want to reduce or increase efficiency of regressor estimator (1.345 corresponds to 95% efficiency: https://cran.r-project.org/web/packages/robustbase/vignettes/psi_functions.pdf ).