ASYMPTOTIC INDEPENDENCE BETWEEN LARGEST AND SMALLEST OF A SET OF INDEPENDENT OBSERVATIONS
SOUTHERN METHODIST UNIV DALLAS TX DEPTOF STATISTICAL SCIENCE
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Let X sub n and X sub l be the largest and smallest order statistics, respectively, of a set of n independent univariate observations. Under rather general conditions, with respect to the distributions of the individual observations, X sub n and X sub l are asymptotically independent. However, asymptotic independence does not occur for all cases.
- Statistics and Probability