Unconventional Background MS Statistics 2021 Profile Evaluation

[movingtostats]

Hi all! I will be applying for Fall 2021 to MS Statistics programs in US and canada. I am however not from a math or stats background. I wanted to know what schools I should be targeting and what are my chances of getting into the best programs like Stanford,Harvard(Biostat), Chicago etc. 

 

Undegrad Institution : University of Delhi (tier 2 college)

Major : Economics

GPA : 7.12/10 (3.6 US equivalent)

Releveant Courses : 

Math/Statistics : Math Econ I (7) ,Math Econ II (8) , Statistics (7), Introductory Econometrics (8), Applied Econometrics (10) 

All grades are out of 10, the two math courses covered some linear algebra and the rest was multivariable calculus but did not have vector calculus stuff like green's theorem. The statistics course was calculus based and had random variables, hypo testing, clt and similar stuff. Econometrics was mostly regression stuff.

Graduate Institution : Indian Statistical Institute

Major : Quantitative Economics ( MS in QE)

Grade : 86/100 (This is only one semester, I rank 4 in a batch of 23.)

Relevant Courses : Math Methods (95), Statistics (95), Game Theory (91), Probability Theory (66)

Math course had good amount of linear algebra, decent amount of real analysis and a lot of optimization topics like KKT. Statistics was taught from Casella & Berger, was very mathematical had things like cramer-rao bound, cramer woldt device, likelihood ratio test, NP lemma etc, Prob Theory was from the stat department and I couldn't do well in it because Real Analysis was a prerequisite which I had not studied, the course had convergence concepts(almost surely,distribution etc) and markov chains.

Relevant courses from this semester are Econometrics I, Theory Of Mechanism Design( not sure how relevant but it is a mathematical course). 

When the time to apply comes I will have had a course in Real Analysis(Analysis-I from the stat dept) and I am pretty sure I'll get an 80+ in it and I will also have had and additional course in Econometrics, one in Sample Survey and and one in Time Series, in my last semester I will also take either Measure Theory or Analysis - II depending on my interest, I cannot take these now or in the next semester as the Institute doesn't allow too many courses from other dept. in one semester.

General GRE : Quant(165), Verbal(164)

GRE Mathematics Subject Test : Not given yet.

The things that I worry about are that my UG institute wasn't really the best in the country, it wasn't a bad school but just wasn't amongst the top colleges, my GPA in UG is also not fabulous however I think it is still better in the relevant courses.  Will bad grade in prob theory be a significant factor?

One thing that I think I have going for me is my Grad School's brand name in Statistics and even in Economics it is the best program in the country and is also the most selective one.

I am also planning to give the GRE Math by studying for it over the summer, I think I should be able to manage 70+(worst case scenario) percentile on this, will this add significant value for top schools because if not then I could intern over the summer and make good money.

LOR : One will be from my game theory and Mechanism Design professor who is a PhD in industrial engineering, rest all will be from economists though should be good.

My dream programs are Stanford MS Statistics, U of Chicago Stats, Harvard Biostats, CMU,U of Washington.

Can you guys tell me about my chances at these schools and also the schools that I should actually apply to . Also what else can I do to improve my chances of getting into the best programs, and should I do a not stats relevant internship in the summer or give the GRE Math, sorry for too many questions.