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  1. I've been wondering why the use of empirical distributions in research is not as prevalent as I think it should be given my understanding (likely misinformed) that an empirical distribution would give the most accurate representation of a data set as opposed to a parametric model.
  2. I think I do recognize the risk of over fitting using empirical distributions but I would also like to think that this risk can be mitigated via bootstrapping methods.

Clearly though, my assumptions must be wrong as I've yet to chance upon any journals that made use of empirical distributions for modelling and deriving conclusions. The question is why is this so? For example, if the black-scholes model fails because the log normal assumption of stock price behavior is not representative, why not use empirical distributions to model stock prices instead of funky jump-diffusion models and so on, which are not always entirely representative as well.

I also wonder if industry practitioners, regardless of background, do actually utilize empirical distributions for their analyses?

Hoping to hear your thoughts.

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    $\begingroup$ Isn't an empirical distribution just effectively like a parametric distribution but with a lot of parameters (the bins)? I imagine several problems when you use many parameters with a problem. Are the parameters accurately estimated when there are many? Do we need all those parameters? $\endgroup$
    – Sextus Empiricus
    Commented Aug 22, 2020 at 23:08
  • $\begingroup$ @SextusEmpiricus Thanks for this wonderful comment and good points. 5 years pass quickly! When i wrote the question, I was still naive about "data driven" approaches. Almost always we will need to formulate some reasonable assumptions about the underlying system before modelling, otherwise we risk overfitting and worse, making decisions based on an endogenously fitted model. $\endgroup$
    – krenova
    Commented Aug 25, 2020 at 18:17

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The empirical (microeconomic) data I am working with currently is incomplete, that is why I try to fit a parametric distribution using extra knowledge on data generation.

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  • $\begingroup$ Thanks for sharing Karsten. What if your data is "kind of" complete. Like daily financial market data, would it provide significant advantage modelling the data using parametric distribution over non-parametric? $\endgroup$
    – krenova
    Commented Jul 21, 2016 at 2:46
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    $\begingroup$ I do not really know, maybe working with non-parametric distributions is more computationally intensive? I like to think of fitting a distribution as (lossy) compressing data. Parametric fitting seems to have a better compression rate, but a higher loss. So it is a trade-off. $\endgroup$
    – Karsten W.
    Commented Jul 21, 2016 at 14:52

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