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On r-quick limit sets for empirical and related processes based on mixing random variables |
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| Authors: | Gutti Jogesh Babu Kesar Singh |
| Affiliation: | 1. Indian Statistical Institute, Calcutta, India;2. Rutgers University USA |
| Abstract: | The r-quick limit points of normalized sample paths and empirical distribution functions of mixing processes are characterized. An r-quick version of Bahadur-Kiefer-type representation for sample quantiles is established, which yields the r-quick limit points of quantile processes. These results are applied to linear functions of order statistics. Some results on r-quick convergence of certain Gaussian processes are also established. |
| Keywords: | r-quick limit points r-quick convergence Gaussian processes Brownian motion empirical process quantile process linear functions of order statistics reproducing kernel Hilbert space φ -mixing strong mixing |
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