No, actually top 30-50 would be fine. I just don't want to be hired at a program without an established stat department.
Does that mean that lots of tenure-track hirings are based on potential, since most people only publish 2-3 papers by the time they defend? What if your advisor is only moderately well-known, but your papers are as good as someone from a top 5 school? Would advisor's reputation matter?
Do faculty selection committees evaluate how consistent your publishing topics are? Can you publish one paper in time series and another in empirical processes and it will seem like a positive? Or will it seem like you are not too organized?