SPACINGS-RATIO EMPIRICAL PROCESSES

We consider an empirical process based upon ratios of selected pairs of spacings, generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on (possibly shifted) intervals of equal lengths, this empirical process converges to a mean-centered Brownian bridge of the form B (C) (u) = B(u)-6Cu(1-u) integral(0) (1) B(s)ds, where B(center dot) denotes a Brownian bridge, and C, a constant. The investigation of the class of Gaussian processes {B (C) (center dot): C R} leads to some unexpected distributional identities such as B(2)(center dot) = (d) B(center dot). We discuss this and similar results in an extended framework.