It is well known that the presence of outliers can mis-estimate (underestimate or overestimate) the overall reserve in the chain-ladder method, when we consider a linear regression model, based on the assumption that the coefficients are fixed and identical from one observation to another. By relaxing the usual regression assumptions and applying a regression with randomly varying coefficients, we have a similar phenomenon, i.e., mis-estimation of the overall reserves. The lack of robustness of loss reserving regression with random coefficients on incremental payment estimators leads to the development of this paper, aiming to apply robust statistical procedures to the loss reserving estimation when regression coefficients are random. Numerical results of the proposed method are illustrated and compared with the results that were obtained by linear regression with fixed coefficients.

中文翻译：

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链梯法的稳健随机系数回归表示

众所周知，异常值的存在可能会错误估计（低估或高估）链梯法中的总体储备，当我们考虑线性回归模型时，假设系数是固定的并且与一次观察相同给另一个。通过放宽通常的回归假设并应用随机变化系数的回归，我们会遇到类似的现象，即对总储量的错误估计。增量支付估计量的随机系数损失准备金回归缺乏稳健性导致了本文的发展，旨在将稳健的统计程序应用于回归系数随机时的损失准备金估计。