Geodesic
On the convergence rate for sums of induced order statistics to the normal law
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part V, Tome 108 (1981), pp. 45-56

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An estimate of the convergence rate of order $1/(\sqrt n)$ for sums of multi-dimensional induced order statistics to the normal law is obtained. 
@article{ZNSL_1981_108_a3,
     author = {V. A. Egorov and V. B. Nevzorov},
     title = {On the convergence rate for sums of induced order statistics to the normal law},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {45--56},
     publisher = {mathdoc},
     volume = {108},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a3/}
}
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V. A. Egorov; V. B. Nevzorov. On the convergence rate for sums of induced order statistics to the normal law. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part V, Tome 108 (1981), pp. 45-56. http://geodesic.mathdoc.fr/item/ZNSL_1981_108_a3/