Test statistics which are almost determined by $o(n)$ tail order statistics are shown to provide tests of asymptotic relative efficiency 0 against the usual type of contiguous alternative. The result is applied to several goodness-of-fit tests: the variance weighted Kolmogorov-Smirnov statistic, the Kolmogorov-Smirnov statistic in the stabilized probability plot and the correlation coefficient in a $Q - Q$ plot for a variety of distributions with exponential tails.
"Overweight Tails are Inefficient." Ann. Statist. 19 (4) 2254 - 2258, December, 1991. https://doi.org/10.1214/aos/1176348397