# Introduction to non-parametric statistics

I have been studying statistics for the past two years. Almost everything I have learnt is about parametric statistics. Now I would like to learn more about non-parametric statistics. Can anyone suggest some concise (perhaps readable as well) introduction into this area?

It depends on what you mean by 'concise', what kind of level of treatment you're seeking (including mathematical vs concepts and intuition), what techniques you want included.

I'd strongly suggest starting with books, and reading more than one book.

Conover's "Practical Nonparametric Statistics" is good, and one I'd definitely lean toward including in any list.

Daniel's "Applied Nonparametric statistics" is very good, reasonably comprehensive for its size.

I found Neave and Worthington's "Distribution-Free tests" very readable when it first came out (and in many ways it still is). Nowadays the code in it looks somewhat dated, but on the other hand, it's generally readable enough to translate. If you can find it it's a good introduction; a worthwhile one to pick up second hand if you don't buy it new.

There are dozens of good books, some older than the three I mentioned, some newer; some may well suit you better than any I've mentioned. I'd start with a university library and browse around on searches with terms like in the above titles, and if possible, see what's nearby.

Read through a few of them and find several you like.

When I did nonparametrics as an undergrad, there were something like eight books in the recommended reading, perhaps more. Every single one of them had something most of the others lacked. I'm glad I had a look at all of them.

If your field of study is in the soft sciences (e.g., psychology, sociology, education), I would recommend Nonparametric Statistics for the Behavioral Sciences by Siegel and Castellan (McGraw-Hill Book Company). (I have the second edition from 1988). From the preface:

A distinctive feature [is] the step-by-step outline of application of each procedure to actual data.

I found "Semiparametric Regression" by Carroll, Wand et al. to be quite readable. It is outdated, but a good thing to start before moving on to Simon Wood's concise, but dense, book on GAMs.

Both these books focus on penalized spline regression models, which isn't everything in nonparametric stats. But arguably most useful for applied people.

• 20826: by way of explanation, just in case you find this answer somewhat confusing - 'nonparametric' can refer not only to unspecified (potentially infinite-parametric) functional form for the distribution (i.e. you don't specify a parametric form for $F_Y(y)$), but also for the relationship between variables ($E(Y)=g(x)$). ACD's answer here refers to the second thing rather than the first. It's actually possible for the term 'nonparametric' in relation to regression models to apply to either issue, or even both at the same time (which I tend to call 'doubly nonparametric'). – Glen_b -Reinstate Monica Mar 16 '14 at 0:21
• right. just curious, what are some examples of instances in applied work where the first of the two forms of nonparametric work might be useful? or I guess the bootstrap would be an example, right? – generic_user Mar 16 '14 at 0:31
• ACD, I recommend you take a look at any of the books mentioned in my answers. I can point - quite literally - to many thousands of papers that apply them to real problems, which include Wilcoxon-Mann-Whitney tests, goodness of fit tests like the Kolmogorov-Smirnov, correlation measures like the Kendall and Spearman, Theil-Sen regression, Kaplan-Meier survival curves (and log-rank tests), permutation/randomization (+other resampling methods) & many more such things. On the whole I'd say may actually be applied quite a bit more often than the sense you use it. Yes, the bootstrap is included. – Glen_b -Reinstate Monica Mar 16 '14 at 0:41
• (ctd) ... the area is quite large; if you narrow it down a bit I can probably find you some particular applications. – Glen_b -Reinstate Monica Mar 16 '14 at 0:45
• Right, so its generally tests that don't rely on distributional assumptions. I guess I wonder if one can estimate a nonparametric distribution for a model at the same time as estimating relationships between variables (probably with a lot of data). But, as you point out, there is a lot to read. – generic_user Mar 16 '14 at 0:59

I was surprised not to see Larry Wasserman's All of Nonparametric Statistics mentioned.

I think it is a great book of relative concise size. Especially if someone already has some background in parametric Statistics this book offers a very fresh look on "statistical methods that aim to keep the number of underlying assumptions as weak as possible". I found it less wordy that other introduction/primer books; this can be a good or a bad thing depending on one's preferences. The only "delta" this book has it is that it does not really cover rank tests.

• (+1) It seems that Wasserman's book "All of Statistics" also contains some, albeit shorter, treatment of the non-parametric statistics. Both those books, as well as many others, are nice, but IMHO an overkill for applied researchers/scientists to some degree. Sure, it won't hurt to know all theorems and proofs, but that's a "nice to have" rather than a "must have", considering time and scope limitations. I'm still yet to find balanced statistical books for applied scientists (that is, rigorous enough without going into too deep of details as well as useful from the application perspective). – Aleksandr Blekh Mar 9 '15 at 5:15