## U-Statistics Based on Spacings

**Authors:** David D. Tung, S. Rao Jammalamadaka

In this paper, we investigate the asymptotic theory for U-statistics based
on sample spacings, i.e. the gaps between successive observations. The
usual asymptotic theory for U-statistics does not apply here because spacings
are dependent variables. However, under the null hypothesis, the uniform
spacings can be expressed as conditionally independent Exponential random
variables. We exploit this idea to derive the relevant asymptotic theory both
under the null hypothesis and under a sequence of close alternatives.
The generalized Gini mean difference of the sample spacings is a prime
example of a U-statistic of this type. We show that such a Gini spacings test
is analogous to Rao's spacings test. We find the asymptotically locally most
powerful test in this class, and it has the same efficacy as the Greenwood
statistic.

**Comments:** 23 Pages.

**Download:** **PDF**

### Submission history

[v1] 18 Jun 2010

[v2] 16 Aug 2010

[v3] 2012-01-11 19:16:15

**Unique-IP document downloads:** 337 times

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