On the asymptotic behaviour of selector statistics

Adaptive procedures proposed by Hogg are based on selector statistics for the skewness and the tails. The asymptotic properties of several proposed selector statistics are investigated. Since ail these statistics have under some assumptions asymptoti¬cally a normal distribution, their properties depend on the asymptotic bias and variance. The reasonable concept to compare the different selector statistics is based on the selection probabil¬ities in discriminating the type of the underlying distribution. These values are numerically calculated and analyzed in detail for a number of underlying distributions.