MICHAEL FALK, MAXIMILIAN ZOTT 20 Moreover, putting c := min$_{i}$$_{=1}$$_{,...,d}$ g$_{i}$ ( t ) > 0, and hence The authors are grateful to two anonymous reviewers for their careful reading of the manuscript. The paper has benefitted a lot from their critical remarks. ∣ ∣$^{ˆ}$ Y ( n ) t ∣ = min i =1 ,...,d ∣ Y ( n ) s$_{i}$ ∣ g$_{i}$ ( t ) ≤ ∣ Y ( n ) s$_{1}$ ∣ c , E ( ( ˆ Y ( n ) t ) 4 ) ≤ 24 c $_{4}$, which completes the proof. □ Acknowledgment References Aulbach, S. , Falk, M. , and Hofmann, M. (2013). On max- stable processes and the functional D -norm. Extremes 16 , 255–283. doi:10.1007/s10687-012-0160-3 . Beirlant, J. , Goegebeur, Y. , Segers, J. , and Teugels, J. (2004). Statistics of Extremes: Theory and Applications . Wiley Series in Probability and Statistics. Wiley, Chichester, UK. doi:10.1002/0470012382 . Billingsley, P. (1999). Convergence of Probability Measures . Wi- ley Series in Probability and Statistics, 2nd ed. Wiley, New York. doi:10.1002/9780470316962 . Brown, B. M. , and Resnick, S. I. (1977). Extreme values of independent sto- chastic processes. J. Appl. Probab. 14 , 732–739. doi:10.2307/3213346 . Cooley, D. , and Sain, S. R. (2012). Discussion of “Statistical modeling of spatial extremes” by A. C. Davison, S. A. Padoan and M. Ribatet. Statist. Sci. 27 , 187– 188. doi:10.1214/12-STS376A . Davison, A. C. , Padoan, S. A. , and Ribatet, M. (2012 a ). Rejoinder. Statist. Sci. 27 , 199–201. doi:10.1214/12-STS376REJ .