On the strong law of large numbers for linear combinations of concomitants

Abstract

The article proves a theorem on the strong law of large numbers for linear functions of concomitants (induced order statistics) for sequences of independent identically distributed two-dimensional random vectors. The result complements previous work by Yang (1981), Gribkova and Zitikis (2017, 2019). The proof is based on the conditional independence property of concomitants Bhattacharya (1974), the strong law of large numbers for functions of order statistics by van Zwet (1980) is used, classical inequalities apply, including Rosenthal’s (1970).