Weighted Approximations for Some Integrated Empirical Processes | ||
| The Egyptian Statistical Journal | ||
| Article 2, Volume 49, Issue 1, June 2005, Pages 19-37 PDF (15.13 M) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.2005.313553 | ||
| Author | ||
| Abd-Elnasser S.A. Rabou* | ||
| Statistics Department, Faculty of Economics & Political Science, Cairo University | ||
| Abstract | ||
| We prove strong and weighted approximations for some newly-defined integrated empirical (IE) processes. Suitable weight functions are incorporated to show the convergence of these processes to their ideal Gaussian processes in the weighted sup-metrics. At first, the approximations were done assuming the processes are constructed from sample with fixed size. Then we derived the approximations from a randomly stopped version of those processes. | ||
| Keywords | ||
| Integrated Empirical Function; Asymptotic Theory; Strong Approximations; Gaussian Processes; Weighted Sup; Norm; Tied; Down Processes; Randomly Stopped Processes | ||
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