The almost sure representation of intermediate order statistics

Summary Let {X _n} be independent and identically distributed and let X _kn ⁽ⁿ⁾ denote the k _n-th order statistic for X ₁ ..., X _n, where k _n but k _n/n0. A representation for X _kn ⁽ⁿ⁾ in terms of the empirical distribution function is developed. The conditions include those under which X _kn ⁽ⁿ⁾ is asymptotically normal.Research partially supported by the University of North Carolina at Chapel Hill under Office of Naval Research Contract No. N00014-75-C-0809 and by The Florida State University under Office of Naval Research Contract No. N00014-76-C-0608.