Analysis Review for Statistics

[klausas]

I'm making the jump from math ed to pure math. I've done a bit more than the usual math-for-teachers stuff and my advisor is convinced I can pull it off, but if I sound nervous, this is why.

I know what to review and study up on before fall semester for two of my classes but I'm at a loss for the third, Mathematical Statistics. The official prerequisite is first semester analysis; the textbook is Hogg, McKean, and Craig. I do not know the professor and am not sure if asking him about this would make the wrong first impression.

It's been a while since I had prob and stat but I think I remember the ideas and will get a reference for formulas and re-memorize the ones that come up. Analysis, though, was supposedly mashed into my calculus coursework; I know (or at least think I know?) that the difference between intro calc and analysis is rigorous reasoning from first principles about the number system, but what I am not sure about is how analysis applies to mathematical statistics as a prereq. If it's just to make sure the students have met axiomatic reasoning and proofwriting before, I'll be OK; I like that sort of thing (and as a result am getting an A in the summer class my advisor told me to take to test my proofwriting skills). On the other hand, if there are specific topics I need from analysis, I'm at a bit of a loss as to which ones.

I have about two weeks relatively clear and would like to be as prepared as possible by the time the semester begins. If anyone can suggest optimal topics to study, I will owe you cookies.

 

[selig5560]

I'm interested in this too, my school also requires Real Analysis 1 for Math. Stats.

 

[klausas]

Over 24 hours and no suggestions...should I post this question somewhere else?

 

[Robert1986]

Well, IMO analysis is a little too much of a pre-req for math stats. I used the same book for my math stat class and I don't think that analysis is required - though it would certainly help. The thing about math stats is that you are going to be doing statistics from the point of view of a mathematician. So, while your intro to prob stat course might have had you memorising a lot of distributions and mgfs and random facts and stuff, you will be deducing these facts for yourself in math stats. Because of this, there is a lot of stuff that deals with series and sequences and so it is a good idea to be solid on those sorts of things. Also, brushing up on multiple integrals will really help a lot, too. Other than reviewing series/sequences and multiple integrals, I can't really think of anything else.

 

[StatGuy2000]

As was said earlier, in mathematical statistics there will be a great deal of emphasis first on establishing a basic understanding of probability theory, which does require an understanding of first year analysis or calculus (I have always though of first year analysis as a slightly more rigorous version of calculus, with an emphasis on proving from first principles).

Mathematical statistics will also place a great deal of emphasis on asymptotics, so a good background in linear algebra will be required for those.