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The scaled [alpha]-Winsorized estimate of exponential scale for censored data: an analysis based on two influence functions

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  • Tableman, Mara
  • Gitelman, Alix I.

Abstract

A new view of the maximum likelihood estimator (MLE) of exponential scale for censored data is presented. This is done by adapting Reid's (Ann. Statist. 9 (1981) 78) approach for obtaining the two influence functions (IF) for the Kaplan-Meier estimate of the survival function; one for uncensored and one for censored data, respectively. The MLEs two IFs are derived. Via this analysis, we propose a new robust estimator, the scaled [alpha]-Winsorized estimator (WE). Under Type II censoring, the WE is the MLE and, hence, is asymptotically efficient in that case. Its two IFs are bounded; hence,WE is B-robust. Its breakdown point is [alpha]. A comparison is made with respect to asymptotic bias and mean square error at contaminated exponential and Weibull survival models.

Suggested Citation

  • Tableman, Mara & Gitelman, Alix I., 2002. "The scaled [alpha]-Winsorized estimate of exponential scale for censored data: an analysis based on two influence functions," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 169-181, September.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:2:p:169-181
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