/sci/ - Science & Math

[Anonymous No.6206557]

Where do I start with statistics from a pure math perspective? I know how to do some computation stats like doing stuff with normal distributions and different hypotheses testing, but I want to get to know the big theorems and their proofs, especially those used in other branches of mathematics.

Any recommendations for what to look at or any books/notes to read? I'm familiar with a standard undergraduate set of math courses (linear algebra, calculus/analysis, etc...) but not so much too advanced (like measure theory).

Thanks.

[Anonymous No.6206742]

Start here: http://mathoverflow.net/questions/31655/statistics-for-mathematicians

[Anonymous No.6206747]

This is good if you already know some collegiate maths:

http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470390638.html

[Anonymous No.6207118]

http://www.amazon.com/All-Statistics-Statistical-Inference-Springer/dp/1441923225

[Anonymous No.6207263]

In my first year we used Casella and Berger, Statistical Inference. It's a pretty standard first-year graduate level stats book.
I know some other places (e.g. Stanford) use Bickel and Doksum, Mathematical Statistics, vol. I and II.

In both cases, there's no measure theory (and, for the most part, no need for it), but the material is covered at a level that will not make a pure math major yawn in boredom. You need to know some probability.

I think what >>6207118 recommends is too elementary. Some of the books cited in the math overflow link are good, even more technical than the C&B and B&D (I remember C&B citing Lehmann's Theory of Point Estimation a few times for tough proofs...) but they tend to be old and dusty. I guess the more politically correct term would be "classical"...

[Anonymous No.6207268]

>>6206557
my 2 cents :
If you want to trully understand the theory behind, you'll need probability theory.
it's mainly based on the axioms of the measure theory.
Another important tool to masterize is the Lebesgue integral.


Once you're done with that, you must know that "statistic" cover a lot of different fields.
Stochastic process, markov' chains are not really the same than sampling and hypo. testing, etc.
Depends on what you want to investigate

[Anonymous No.6208062]

>>6207268
Where should I learn measure theory and how much of it?

[Anonymous No.6208871]

>>6208062
this should cover your needs

http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf

Only chapter 1, and 1.7 can be skipped for the moment IMO.