Some new almost sure results on the functional increments of the uniform empirical process

Details Some new almost sure results on the functional increments of the uniform empirical process Some new almost sure results on the functional increments of the uniform empirical process

2012-01-26

arxiv.org/abs/1201.5516v1

Mathematics

Statistics Theory

Scientific paper

Given an observation of the uniform empirical process $\alp_n$, its functional increments $\alp_n(u+a_n\cdot)-\alp_n(u)$ can be viewed as a single random process, when $u$ is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate versions of these processes as $\nif$ and $a_n\downarrow 0$. Under mild conditions on $a_n$, a convergence in distribution and functional limit laws are established. The proofs rely on a new extension of usual Poissonisation tools for the local empirical process.

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