Good resources (online or book) on the mathematical foundations of statistics Before I ask my question, let me give you a bit of background about what I know about statistics so that you have a better sense of the types of resources that I'm looking for.
I'm a graduate student in psychology, and as such, I use statistics almost every day.  By now I'm familiar with a pretty broad array of techniques, mostly as they are implemented in the general structural equation modeling framework.  However, my training has been in the use of these techniques and the interpretation of results -- I don't have much knowledge of the formal mathematical foundations of these techniques.
However, increasingly, I've had to read papers from statistics proper.  I've found that these papers often assume a working knowledge of mathematical concepts that I don't know much about, such as linear algebra.  I have therefore become convinced that if I wish to do more than blindly use the tools that I have been taught, it would be useful for me to learn some of the mathematical basis of statistics.
So, I have two related questions:


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*What mathematical techniques would be useful for me to know if I want to brush up on the mathematical foundation of statistics?  I've encountered linear algebra pretty often, and I'm sure that learning about probability theory would be useful, but are there any other areas of math that would be useful for me to learn about?

*What resources (online or in book form) can you recommend to me as someone who wants to know more about the mathematical foundations of statistics?

 A: Some important mathematical statistics topics are: 


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*Exponential family and sufficiency.

*Estimator construction.

*Hypothesis testing. 


References regarding mathematical statistics:


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*Mood, A. M., Graybill, F. A., & Boes, D. C. (1974). Introduction to theory of statistics. (B. C. Harrinson & M. Eichberg, Eds.) (3rd ed., p. 564). McGraw-Hill, Inc.

*Casella, G., & Berger, R. L. (2002). Statistical Inference. (C. Crockett, Ed.) (2nd ed., p. 657). Pacific Grove, CA: Wadsworth Group, Thomson Learning Inc.
A: Have a look at the Mathematical Biostatistics Bootcamp at Coursera https://www.coursera.org/#course/biostats.
A: Maths:
Grinstead & Snell, Introduction to Probability (it's free)
Strang, Introduction to Linear Algebra
Strang, Calculus
Also check out Strang on MIT OpenCourseWare.
Statistical theory (it's more than just maths):
Cox, Principles of Statistical Inference
Cox & Hinkley, Theoretical Statistics
Geisser, Modes of Parametric Statistical Inference
And I second @Andre's Casella & Berger.
A: SEM is (in my opinion) very far removed from traditional probability theory and some basic statistical techniques that extend easily from it (such as point estimation, large sample theory, and Bayesian statistics). I think SEM is the result of a great deal of abstraction from such methods. I furthermore think that the reason why such abstractions were necessary was because of the overwhelming demand to better understand causal inference.
I think a book that would be perfect for someone of your background would be Judea Pearl's Causality. This book specifically addresses SEM as well as multivariate statistics, develops a theory of causality and inference, and is very philosophically sound. It's not a mathematical book, but draws heavily upon logic and counterfactuals, and develops a very precise language for defending statistical models. 
I can say from a mathematical background that these results are very sound and do not require an extensive understanding of calculus. I also think it's unrealistic for someone of your pedigree to catch up on the necessary mathematics when you're already a graduate student, that's why there are statisticians!
