I have a normal sample but that is contaminated in the left and the right tails (no more than 2.5% each). The contamination gives rise to high and low values. I wanted to know what methods I have in order to estimate ths sigma of the N(0, sigma^2) distribution. I have looked at R's vignettes but almost all the examples there are on different aspects of linear and other models. I am looking for a simple estimate of the scale parameter of the distribution in the presence of at most 5% contaminants. I can use something crude like 1.5 times median of the absolute values of the inner 95% but I was wanting something more precise and specific. Any suggestions? Thanks in advance for any help!

  • $\begingroup$ You already know the distribution is not Normal, but still you want an estimator for the standard deviation of an effective Normal? $\endgroup$ Apr 8, 2019 at 5:41
  • $\begingroup$ I do know that the inner 95% is normal. The contamination is not, nor is it from one distribution but I know that they are from distributions with means larger than 0 in absolute value. $\endgroup$ Apr 8, 2019 at 12:14
  • $\begingroup$ Strongly smells the homework. Use a trimmed variance (there will be a bias, I have no idea how to correct). $\endgroup$
    – user65203
    Apr 8, 2019 at 12:21
  • $\begingroup$ Nope, this is not a HW problem, it is much more complicated than that. I found a good lead in DOI: 10.1111/j.1541-0420.2008.01064.x which is for K groups but can be modified. Another option is to solve using EM (perhaps the best option) but computationally intensive. $\endgroup$ Apr 8, 2019 at 15:09


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