Asymptotic spacings theory with applications to the two‐sample problem

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Abstract
The asymptotic distribution theory of test statistics which are functions of spacings is studied here. Distribution theory under appropriate close alternatives is also derived and used to find the locally most powerful spacing tests. For the two‐sample problem, which is to test if two independent samples are from the same population, test statistics which are based on “spacing‐frequencies” (i.e., the numbers of observations of one sample which fall in between the spacings made by the other sample) are utilized. The general asymptotic distribution theory of such statistics is studied both under the null hypothesis and under a sequence of close alternatives.