Penalizing outliers in a dataset I have a dataset of ages ranked from smallest to highest. Next to each entry, I have calculated the respective ranked percentile. I then have to remove all values above the 99.5% percentile from the dataset (i.e. what we deem as outliers). Once these have been removed, I have to recalculate the ranked percentile values for the remaining entries, such that the new highest value has a percentile value of 1 (or 100%). For the outliers that were removed, I have to somehow penalize these values and then assign a percentile value based on the remaining data.
I have not come across any method in statistics of "penalizing" outliers, however, I have been asked to do this. Is there such a method of "penalizing" outliers in statistics, apart from removing the outliers completely?
 A: Well if we think of regularization, than high coefficients will be penalized. How do we get high coefficients, maybe through outliers which distort the mean impact of a variable.
One way I could think of, that the type of regression will automatically penalize for such a case, and that we have a regularization on the outlier. Maybe you start your search for regularization of outliers to get more info.
If you should really use weights to penalize your age, then you could define every age below the threshold with a w0=1 and all other values above that threshold  with a rising declining weight.
in market research when we try to get e represntative data set we do the same with some sorts of working class (we weight them up) so they represent a specific ratio of a speciic workerclass in the country, if we didn't get enough ppl in our dataset of that workerclass/proportion.
In summary: all i can think of is regularization of outliers. like for coefficients in lasso and ridge. But I have the feeling that would be done somehow automatically if the coefficient is pushed e.g. to zero, but I made no experiments on that. may be one of the other collagues here has a different insight.
Update:
This link however tells exactly, the same with regularization what i mentioned previously ago: maybe you have a look at it.
https://datascience.stackexchange.com/questions/63900/how-regularization-helps-to-get-rid-of-outliers
