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Approximation of Kolmogorov-Smirnov Test Statistics

Probability 2018-02-27 v1

Abstract

Motivated by the weak limit of the Kolmogorov-Smirnov test statistics, in this contribution, we concern the asymptotics of \begin{align*} \mathbb{P}\left\{\sup_{\boldsymbol{x}\in [0,1]^n}\left(W(\boldsymbol{x})\Big| W(\boldsymbol{1})=w\right)>u\right\}, \ w\in\mathbb{R}, \end{align*} for large uu where W(x)W(\boldsymbol{x}) is the multivariate Brownian sheet based on a distribution function FF. The results related to general FF are investigated and some important examples are also showed.

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Cite

@article{arxiv.1802.08883,
  title  = {Approximation of Kolmogorov-Smirnov Test Statistics},
  author = {Long Bai and David Kalaj},
  journal= {arXiv preprint arXiv:1802.08883},
  year   = {2018}
}

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