Does having Measure Theory in your transcript give your PhD application an edge?

[Bayequentist]

Real Analysis is a must-have for a PhD application to a strong statistics program. What about Measure Theory? In general, how do PhD admission committees view applicants that have completed difficult and relevant graduate-level coursework in mathematics? I'm asking this because I'm trying to decide between taking Multivariate Data Analysis and Measure Theory.

[Geococcyx]

Yeah, measure theory would do you a lot more help admissions-wise than multivariate would.  I'm not an expert, but I'm pretty sure this meshes with everything the experts on here say.

Edited February 22, 2019 by Geococcyx

[Stat Assistant Professor]

It isn't necessary to have, but if you think you can get an A in measure theory, then that should definitely help your PhD application. It might actually give you a bit of a "headstart" in the measure-theoretic probability class you'll have to take in a PhD program, because you will already know what measure spaces, Lebesgue measures, counting measures, and product measures are and how to read notation involving the Lebesgue integral. And you will have already seen stuff like Fubini's Theorem or Fatou's lemma.

What kind of PhD programs are you targeting? It would probably help you the most for some places like Stanford, University of Chicago, or UPenn Wharton. For other programs, it's probably more important to have straight A's than to have measure theory on your transcript.

[Bayequentist]

29 minutes ago, Stat PhD Now Postdoc said:

It isn't necessary to have, but if you think you can get an A in measure theory, then that should definitely help your PhD application. It might actually give you a bit of a "headstart" in the measure-theoretic probability class you'll have to take in a PhD program, because you will already know what measure spaces, Lebesgue measures, counting measures, and product measures are and how to read notation involving the Lebesgue integral. And you will have already seen stuff like Fubini's Theorem or Fatou's lemma.

What kind of PhD programs are you targeting? It would probably help you the most for some places like Stanford, University of Chicago, or UPenn Wharton. For other programs, it's probably more important to have straight A's than to have measure theory on your transcript.

I’m mostly targetting programs ranked around 11~30. So you’re saying it’s better for me to take methods classes and aim for straight A’s rather than difficult math classes?

[Bayequentist]

1 hour ago, Geococcyx said:

Yeah, measure theory would do you a lot more help admissions-wise than multivariate would.  I'm not an expert, but I'm pretty sure this meshes with everything the experts on here say.

Do you think it’s still worth it even if I’m not guaranteed to get an A (like A- or B+)?

Edited February 23, 2019 by Bayequentist

[Stat Assistant Professor]

1 minute ago, Bayequentist said:

I’m mostly targetting programs ranked around 11~30. So you’re saying it’s better for me to take methods classes and aim for straight A’s rather than difficult math classes?

If you think you are more likely to get an A in the multivariate class, then I would take that. PhD programs will teach you the measure theory that you need to know in your measure-theoretic probability theory class, so it isn't strictly necessary to have learned it before enrolling.

Plus, the programs ranked in the 11-30 range are more willing to accept applicants from non-stat/non-math backgrounds (e.g. students who majored in economics, engineering, or physics), and I would guess that almost none of those applicants who were accepted have taken measure theory previously. 

[Bayequentist]

8 hours ago, Stat PhD Now Postdoc said:

If you think you are more likely to get an A in the multivariate class, then I would take that. PhD programs will teach you the measure theory that you need to know in your measure-theoretic probability theory class, so it isn't strictly necessary to have learned it before enrolling.

Plus, the programs ranked in the 11-30 range are more willing to accept applicants from non-stat/non-math backgrounds (e.g. students who majored in economics, engineering, or physics), and I would guess that almost none of those applicants who were accepted have taken measure theory previously. 

I've realized that I have the option to take Measure Theory on a pass/fail basis, and it would be a non-major elective course. It would be considered voluntary coursework that does not count toward my degree's completion. What do you think of applicants who have Measure Theory on their transcript with a grade of P? Do you think it's worth it?

[Stat Assistant Professor]

4 hours ago, Bayequentist said:

I've realized that I have the option to take Measure Theory on a pass/fail basis, and it would be a non-major elective course. It would be considered voluntary coursework that does not count toward my degree's completion. What do you think of applicants who have Measure Theory on their transcript with a grade of P? Do you think it's worth it?

I don't think a "P" will mean much to the adcoms, because it doesn't give any indication whether you did exceptionally or whether you just did the bare minimum to pass. Also, graduate school grades are somewhat inflated, so do not take this class for a letter grade if you are not confident you can get an "A" in it.

If you are very interested in the subject, you could ask the professor to audit the class. In my experience, simply auditing is not a good way to learn though -- to really learn measure theory (and most subjects within math), you need to actually practice and do the problem sets. If you don't think you will have time, then I would just not bother with it and wait until you are in a Statistics PhD program to learn it.