On Small Samples and the Use of Robust Estimators in Loss Reserving

This paper explores the use of robust location estimators such as Average-Excluding-High-And-Low and Huber's M-estimators in loss reserving. Standard order statistics results are used to investigate the finite-sample properties of Average-Excluding-High-And-Low for positively skewed distributions including bias and effciency, based on the criterion of mean squared error. The paper concludes that Averages-Excluding-High-And-Low, although biased with respect to the population mean for positively skewed distributions, is more effcient than the sample average in small samples. The paper also shows that the use of Huber's M-estimators can enhance the consistency in loss development factor selections by identifying the implied risk preference.

Keywords: Robust Estimators; Order Statistics; Averages-Excluding-High-And-Low; Huber's M-Estimators; Loss Reserving.