Before revision:  The new estimator can under mild conditions exhibit a rate of convergence in probability equal to n^{ -(p-1) /( 2p-1 )}, where p\ge 2 is an integer that indexes the strength of certain smoothness assumptions.
After revision:  The new estimator can under mild conditions exhibit a rate of convergence in probability equal to n^{ -(p-1) /( 2p+1 )}, where p\ge 2 is an integer that indexes the strength of certain smoothness assumptions.