Chances of getting in to top statistics graduate programs (i.e. global top 20)?

[hopesandprayers]

TL;DR - What are my chances of getting into a top statistics graduate program (either masters or doctorate) with excellent marks but little research experience?

I am a student at a Canadian university ranked 151-200 in mathematics and statistics (on QS at least).  My major is statistics.  My GPA is a 4.30 out of a possible 4.33, and I have A+ grades in every math and stats course I have ever taken, obviously these include: calc I-III, intro algebra (theoretical version), ODEs, intro complex analysis, real analysis I and II, regression, time series, probability theory, multivariate stats.  If I maintain my current GPA I am likely going to graduate inside the top three people in my graduating class (top GPA in grads this summer was 4.29).

I graduate next year, but only have one semester of research experience and no publications.  I am curious, for the sake of my ambitions and time + application money's sake, how likely am I to get into a top school such as Stanford/Harvard/Princeton, etc. for statistics or mathematics?  I imagine mathematics (or CS) requires more of a research background than the stats does (this is coming from the advisor at my university and my research supervisor for the one semester I have).

I appreciate any advice you guys can give.  Thanks!