This is just a copypasta of a post I made to Kaggle.com/fourms. It got no responses in 6 days! Maybe it was just a bad question? Anyway, any material you can recommend would be appreciated...
First post, so please be gentle. Also, keep in mind I only went for a math minor (finance major).
OK, so up until last week I had no idea non-parametric statistics even existed. As far as my preliminary research has indicated, unlike parametric statistics, non-parametric statistics do not use distributions to make inference about a total population from a sample (and also predominately use medians in lieu of means).
After taking abstract algebra and some discrete mathematics, I am fairly competent with set theory and cantor notation. I also took an advanced logic class covering methods of proof ("reductio ad absurdum" and all that).
All the texts I have found refer to "assumptions" that must be true in order to apply parametric statistics to a sample, but they don't go over what these are or how to test for them!
Can you guys recommend a book(s) that...
- Enumerates the assumptions made by parametric models (Gauss, F, T, Z, etc), describes how to test for these with set theory (preferably cantor notation), and does a good job of delineating these proofs.
- A book which acts as a road-map for different statistical techniques, which assumes absolute familiarity with basic parametric statistics. What I have found so far has been so rudimentary, I spend all my time re-reading verbose descriptions of basic stat.
Perhaps incorrectly, I am basing much of my current understanding off these two finds during my googling:
Any input would be appreciated!