ON THE ROBUST ESTIMATOR OF THE POPULATION MOMENTS
Keywords:
Huber m-estimation, population moments, robust estimator, trimmed meanAbstract
This paper proposed the Huber’s M-estimator for estimating the population moments mk . The Estimates using Huber’s M-estimator were compared to the classical estimator of the population moments. Eleven features of the population moments from twelve probability distributions and mean squared error were computed to compare the two estimators. For the Huber’s M-estimator, we used the trimming proportions p = 0.05, 0.10, 0.15, 0.20 and 0.25 and compute the estimates for n=20, 30, and 100. The result confirms that the appropriate estimator of the population moments for the symmetric distributions is classical while the estimator with trimming proportion p = 0.25 is appropriate for the asymmetric distributions. Furthermore, the estimators with higher trimming proportions give smaller variances as compared to the estimators that have lower trimming proportions.
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http://math.uprm.edu/wrolke/esma6665/robust.htm
http://math.uprm.edu/wrolke/esma6665/robust.htm
http://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm
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http://www.itl.nist.gov/div898/handbook/eda/section3/eda366.htm
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