(2005). Weighted Approximations for Some Integrated Empirical Processes. test, 49(1), 19-37. doi: 10.21608/esju.2005.313553
. "Weighted Approximations for Some Integrated Empirical Processes". test, 49, 1, 2005, 19-37. doi: 10.21608/esju.2005.313553
(2005). 'Weighted Approximations for Some Integrated Empirical Processes', test, 49(1), pp. 19-37. doi: 10.21608/esju.2005.313553
Weighted Approximations for Some Integrated Empirical Processes. test, 2005; 49(1): 19-37. doi: 10.21608/esju.2005.313553

Weighted Approximations for Some Integrated Empirical Processes

The Egyptian Statistical Journal
Article 2, Volume 49, Issue 1, June 2005, Pages 19-37
Document Type: Original Article
DOI: 10.21608/esju.2005.313553
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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