I'd like to argue why the outliers in this case can be (at least partially) ignored. One topic-independent argument would be simply the sparsity of the data, giving the outliers exaggerated importance. I would like to make a stronger argument with connection to options though.
My reasoning, from what I gathered through a little research, is something along the lines of: the OTM options are by their nature more likely to create anomalies like this since they are very risky and likely to be traded by amateurs who are attracted by low option premiums. Thus an outlier is less likely to hold valuable information about the market. Whether that makes (any) sense and whether that could create this effect in the IV is not something I can decide with my lack of theoretical and empirical knowledge about this topic.
Am I at least somewhat correct? What would be a correct argument? Is there some literature backing up the statements?
It's entirely possible I'm missing something or am completely wrong. If that's the case, is there an argument to be made to the same effect?
Please answer in simple terms. I am a student of mathematics so I can deal with mathematical complexity, but have very little knowledge of financial derivatives.
Thank you very much!