Asymptotic efficiency of the goodness-of-fit test based on linear statistics

A huge literature about the Pitman’s asymptotic efficiencies (AE) of the goodness-of-fit tests based on higher-order non-overlapping spacings is available. The performance of the linear random variable based on higher-order non-overlapping spacings is measured asymptotically. Since the linear test satisfy the Cramér’s condition so the probability of Large Deviation results are applicable for this statistics. It is observed that just like Pitman’s sense, Linear test in intermediate (all three cases) is most efficient as well because it satisfies the above mentioned condition.