Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7547331 | Journal of Statistical Planning and Inference | 2018 | 11 Pages |
Abstract
For a set of iid U(0,1)-distributed random variables we introduce a normal beta-transformed uniform empirical process. The new process possesses the property that it is normally distributed in all order statistics. We show that this process converges to a standardized Brownian bridge in the central range and large parts of the intermediate range. Moreover, it coincides asymptotically on a suitable interval with the well-known normalized versions of the uniform empirical and uniform quantile process. It remains an open question whether the convergence of the new process to a standardized Brownian bridge may be even better than for empirical and quantile processes. The supremum of the normal beta-transformed process coincides with a special statistic of a goodness-of-fit (GOF) test with so-called equal local levels. Recent results show that such GOF tests have favorable properties compared to GOF tests based on empirical and quantile processes.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Veronika Gontscharuk, Helmut Finner,