The Influence Functions and Breakdown Points of the L-Moments, Tl-Moments and the LQ-Moments Estimators | ||||
| The Egyptian Statistical Journal | ||||
| Article 3, Volume 55, Issue 1, June 2011, Page 22-39 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2011.314309 | ||||
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| Abstract | ||||
| The L-moments are defined as linear combinations of expected values of order statistics of an absolutely continuous random variable, (Hosking 1990). The advantages of L- moments over classical moments are: able to characterize a wider range of distributions; and the L-moments estimators are "more robust to the presence of outliers". Elamir and Seheult (2003) introduced an extension of L-moments called TL-moments. TL-moments estimators are assumed to be "more robust against outliers" than L-moments estimators. Mudholkar and Hutson (1998) introduced LQ-moments estimators as a "robust" version of the I- moments estimators. It is essential to study robustness of the above estimators according to the basic criteria to assess robustness. Namely, an estimator is locally robust if its influence function is bounded with small gross-error sensitivity. An estimator is globally robust if its breakdown point is large. In this paper we derive the influence function and the breakdown point for the L-moments, the LQ-moments and the TL-moments estimators. | ||||
| Keywords | ||||
| L-Moments - Tl-Moments - Ql-Moments - Influence Function - Gross Error; Sensitivity - Breakdown Poin | ||||
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