2
$\begingroup$

I am learning statistical inference by myself, I have skim through a few books like Casella Hoggs and I find it omitted lots of details, for example, they didn't introduce the conditional expectation, so there are only proofs in discrete case about "sufficient statistics " "factoring theorem ", etc. could you recommend me a book for graduates or doctor degree? thanks!

background: I'm a first-year graduate student working on probability.

$\endgroup$
3
  • $\begingroup$ Perhaps this question rather belongs to stats.stackexchange.com? Also, I think if you give out more info on your background you might have more helpful answers. $\endgroup$
    – snoram
    Mar 31, 2016 at 12:06
  • 1
    $\begingroup$ I am doing a PhD in econometrics and I really like "Probability and Measure" by Patrick Billingsley. This is not so much a statistics as a probability theory book though. A high level statistics book is basically any book by van der Vaart, for example "Asymptotic Statistics". As Snoram says, if you provide some more information about what you exactly want we could provide you with more information on books. $\endgroup$
    – Marc
    Mar 31, 2016 at 12:10
  • $\begingroup$ math.stackexchange.com/q/51785/321264 $\endgroup$
    – StubbornAtom
    Apr 22, 2020 at 19:11

1 Answer 1

Reset to default
1
$\begingroup$

I think you can try to follow the OCW course:

http://ocw.mit.edu/courses/mathematics/18-466-mathematical-statistics-spring-2003/syllabus/

You are certainly right that most introductory statistics books do not use measure theory rigorously, and it is a bit annoying if you knew it already. But if you go through the proofs in the above notes, you will find most are (in my opinion) abstract nonsense with no examples. So like calculus is more useful than real analysis for engineer majors, introductory statistics (in some sense) is more useful than abstract mathematical statistics. I noticed you already asked on cross-validated, so perhaps no need to compile a separate long list at here. As you can see the subject branches off very quickly and what you are looking for depends a lot on your academic interest.

Enjoy!

$\endgroup$
2

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .