In this paper we investigate the tail behaviour of a random variable S which may be viewed as a functional T of a zero mean Gaussian process X, taking special interest in the situation where X obeys the structure which is typical for limiting processes occurring in nonparametric testing of...

Wieand's theorem on equivalence of limiting approximate Bahadur efficiency and limiting Pitman efficiency is extended in several ways. Conditions on monotonicity and continuity are obviated, composite null hypotheses are incorporated, and the implications of a weaker form of Wieand's Condition...

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