In this note we include a correction for Equation (19) on page 840 which is a step in the proof of Theorem 4 of Fan et al.(2014). There is no change in the statement of Theorem 4, and the rest of the proof stays unchanged. Equation (19) on page 840 should be corrected to as follows: We apply the coordinatewise mean-value theorem with respect to each coordinate of (ie, j) to obtain that