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I have a large simulated loss data (from catastrophic models developed at my school) to calculate some extreme quantiles. Previously they used non-parametric methods to do this (find the point estimate for these extreme quantiles and CIs).

I am using parametric models (extreme value theory, fat tail distributions, etc.) to do it. I have been thinking about the pros and cons for these two methods.

I would appreciate if someone could provide some summaries of parametric and non-parametric models, their advantages and disadvantages.

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    $\begingroup$ @melon. Your question is quite vague. What do you mean by parametric and non parametric? (i know of a few different ways in which these terms are used). $\endgroup$ – richiemorrisroe May 7 '11 at 7:32
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    $\begingroup$ @richie Out of curiosity--given that there is a standard meaning of parametric statistics--what different kinds of usage do you have in mind? It seems to me this question is sufficiently clear and well posed, but what you (and @Fr in a reply) may be objecting to is that it is too broad and would benefit from being narrowed. @Melon Do you have a particular context, problem, or example in mind that would help focus this question? $\endgroup$ – whuber♦ May 8 '11 at 15:05
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    $\begingroup$ "Nonparametric" is a pretty big umbrella, covering everything from rank-sum tests to kernel regression to infinite mixture models, etc. A little clarification/context would buy better answers, I think. $\endgroup$ – JMS May 9 '11 at 1:57
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    $\begingroup$ @richie I am grateful for that insight. I wasn't aware that using "non-parametric" with certain audiences could potentially cause miscommunication. That's something I'll watch out for in the future. $\endgroup$ – whuber♦ May 9 '11 at 14:47
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    $\begingroup$ @richie Page 286 of Julie Pallant's SPSS Survival Manual equates "nonparametric" with "distribution-free" and gives a partially correct definition (to wit, it asserts nonparametric techniques "do not make assumptions about the underlying population distribution," which actually is true of very few nonparametric methods). However, it doesn't go so far as to equate "nonparametric" with "not using the normal distribution." Were you perhaps referring to a different "survival guide"? $\endgroup$ – whuber♦ Jul 11 '11 at 18:29
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In my experience, they are both useful in different situations.

Where you can confidently say that the data come from a specified probability model, then parametric statistics will usually give you more information. However, they can also lead to significantly biased conclusions if the wrong model is used.

Non-parametric statistics, on the other hand, require fewer assumptions about the data, and consequently will prove better in situations where the true distribution is unknown or cannot be easily approximated using a probability distribution.

All in all, I prefer making as few assumptions as possible, so I tend to prefer non-parametric approaches.

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  • $\begingroup$ I have a large simulated loss data (from catastrophic models developed at my school) to calculate some extreme quantiles. previously they used non-parametric methods to do this (find the point estimate for these extreme quantiles and CIs). I am using parametric models (extreme value theory ,fat tail distributions etc) to do it. I have been thinking about the pros and cons for these two methods. I appreciate all your help $\endgroup$ – Melon May 10 '11 at 17:18
  • $\begingroup$ @ Melon if you add your comment to your question above, you are far more likely to get better responses. $\endgroup$ – richiemorrisroe May 10 '11 at 17:49
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The question is too vague as such, but any answer will depend on your object of study (example). You will find tons on the topic over at Andrew Gelman's blog, with an April's Fool somewhere in the middle if I recall correctly.

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