Ferger, D.; Vogel, D. Weak convergence of the empirical process and the rescaled empirical distribution function in the Skorokhod product space. (English. Russian original) Zbl 1239.60019 Theory Probab. Appl. 54, No. 4, 609-625 (2010) and Teor. Veroyatn. Primen. 54, No. 4, 750-770 (2009). The authors consider the joint weak convergence of the empirical process and the rescaled empirical distribution function. They show that the pair of these processes converges to a limit having two independent components, namely, a time-transformed Brownian bridge and a two-sided Poisson process. In the discussion, the authors point out that the asymptotic independence is a rather unexpected result.To prove the limit statement, they develop a short weak convergence theory for the Skorokhod product space; here, the classical criteria convergence of finite-dimensional distributions and tightness are formulated for the product space.The paper ends with an example showing how the result can be used in statistics. Reviewer: Hannelore Liero (Potsdam) Cited in 4 Documents MSC: 60F05 Central limit and other weak theorems 60G99 Stochastic processes 62M99 Inference from stochastic processes Keywords:Brownian bridge; empirical process; finite-dimensional distribution; Poisson process; Skorokhod topology; tightness PDFBibTeX XMLCite \textit{D. Ferger} and \textit{D. Vogel}, Theory Probab. Appl. 54, No. 4, 609--625 (2010; Zbl 1239.60019) Full Text: DOI arXiv