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Estimation of total time on test transforms for stationary observations

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  • Csörgo, Miklós
  • Yu, Hao

Abstract

By proving Chibisov-O'Reilly-type theorems for uniform empirical and quantile processes based on stationary observations, we establish a nonparametric large sample estimation theory for total time on test transforms. In particular, we obtain weak approximations for total time on test transforms also under the assumption of positively associated dependence, a kind of dependence that is encountered in many practical life testing situations. We derive similar asymptotic results for mixing sequences as well, another and often used structure of dependence for sequences.

Suggested Citation

  • Csörgo, Miklós & Yu, Hao, 1997. "Estimation of total time on test transforms for stationary observations," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 229-253, June.
  • Handle: RePEc:eee:spapps:v:68:y:1997:i:2:p:229-253
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    References listed on IDEAS

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    1. Shao, Qi-Man & Yu, Hao, 1993. "Bootstrapping the sample means for stationary mixing sequences," Stochastic Processes and their Applications, Elsevier, vol. 48(1), pages 175-190, October.
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