Asymptotic normality of linear combinations of functions of the concomitant order statistics

In this note we derive asymptotic normality for a class of linear combinations of functions of concomitant order statistics by exploiting the relation between these statistics and rank statistics for testing independence. The proof can at once be obtained from the proof of the asymptotic normality (under fixed alternatives) of the statistics of the latter type by a slight modification which is in fact a simplification. The score function is allowed to have a finite number of discontinuities (so that one- or two- sided trimmed means are included) and need not be bounded. In this way we prove results similar to those in Yang (1981b) in a different and simple manner.

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