Does anyone know an outlier detection method for a univariate categorical (nominal, unordered) statistical variable? Without any assumptions about the categorical variable distribution (non-parametric method)?
Outliers are extreme values that we come across, where they may be influential to the model or not. When it comes to categorical data (say Gender: as in male and female). There's no way of any outlier detection in that. If you mean something like this: You take a sample of 10 with 9 males and 1 female. So you mean that "1 female" is an outlier? NO! It's just the composition of the sample which you have selected.
Think about your question once more because you ask for an algorithm to detect which of these is an outlier:
Nominal scale means that you have just labels of items like city names or car brands. You can't tell which is an outlier without additional info.