This paper concerns squared M_split(q) estimation and its robustness against outliers. Previous studies in this field have been based on theoretical approaches. It has been proven that a conventional analysis of robustness is insufficient for M_split(q) estimation. This is due to the split of the functional model into q competitive ones and, hence, the estimation of q competitive versions of the parameters of such models. Thus, we should consider robustness from the global point of view (traditional approach) and from the local point of view (robustness in relation between two “neighboring” estimates of the parameters). Theoretical considerations have generally produced many interesting findings about the robustness of M_split(q) estimation and the robustness of the squared M_split(q) estimation, although some of features are asymptotic. Therefore, this paper is focused on empirical analysis of the robustness of the squared M_split(q) estimation for finite samples and, hence, it produces information on robustness from a more practical point of view. Mostly, the analyses are based on Monte Carlo simulations. A different number of observation aggregations are considered to determine how the assumption of different values of q influence the estimation results. The analysis shows that local robustness (empirical local breakdown points) is fully compatible with the theoretical derivations. Global robustness is highly dependent on the correct assumption regarding q. If it suits reality, i.e. if we predict the number of observation aggregations and the number of outliers correctly, then the squared M_split(q) estimation can be an alternative to classical robust estimations. This is confirmed by empirical comparisons between the method in question and the robust M-estimation (the Huber method). On the other hand, if the assumed value of q is incorrect, then the squared M_split(q) estimation usually breaks down.

本文涉及平方M _split（q）估计及其对异常值的鲁棒性。在该领域的先前研究已经基于理论方法。已经证明，鲁棒性的常规分析不足以进行M _split（q）估计。这是由于将功能模型拆分为q个竞争模型，因此估算了此类模型的q个竞争模型的参数。因此，我们应该从全局角度（传统方法）和局部角度（参数的两个“相邻”估计之间的稳健性）考虑稳健性。理论上的考虑通常产生了关于M _split（q）的鲁棒性的许多有趣发现。估计和平方M _split（q）估计的鲁棒性，尽管某些特征是渐近的。因此，本文着重于平方M _split（q）的鲁棒性的实证分析。有限样本的估计，因此，从更实际的角度来看，它会产生关于鲁棒性的信息。通常，这些分析基于蒙特卡洛模拟。考虑使用不同数量的观察汇总来确定q的不同值的假设如何影响估计结果。分析表明，局部鲁棒性（经验局部击穿点）与理论推导完全兼容。全局鲁棒性高度依赖于有关q的正确假设。如果它适合现实，即如果我们正确地预测了观测集合的数量和离群值的数量，则平方M _split（q）估计可以替代经典鲁棒估计。这通过相关方法与鲁棒M估计（Huber方法）之间的经验比较得到了证实。另一方面，如果q的假定值不正确，则平方的M _split（q）估计值通常会崩溃。