For rank-correlation M-estimators with U-process objectives, estimation works at the sqrt(p/n) rate when p/n converges to zero, but normal approximation needs the much stronger condition log(n/p^2) p^{3/2}/n^{1/4} to converge to zero.
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On rank estimators in increasing dimensions
For rank-correlation M-estimators with U-process objectives, estimation works at the sqrt(p/n) rate when p/n converges to zero, but normal approximation needs the much stronger condition log(n/p^2) p^{3/2}/n^{1/4} to converge to zero.