The restricted polynomially-tilted pairwise interaction (RPPI) distribution gives a flexible model for compositional data. It is particularly well-suited to situations where some of the marginal distributions of the components of a composition are concentrated near zero, possibly with right skewness. This article develops a method of tractable robust estimation for the model by combining two ideas. The first idea is to use score matching estimation after an additive log-ratio transformation. The resulting estimator is automatically insensitive to zeros in the data compositions. The second idea is to incorporate suitable weights in the estimating equations. The resulting estimator is additionally resistant to outliers. These properties are confirmed in simulation studies where we further also demonstrate that our new outlier-robust estimator is efficient in high concentration settings, even in the case when there is no model contamination. An example is given using microbiome data. A user-friendly R package accompanies the article.

翻译：受限多项式倾斜成对交互（RPPI）分布为成分数据提供了灵活的建模框架，尤其适用于成分分量边际分布集中于零附近且可能呈现右偏态的场景。本文通过融合两种思路，发展了一种可处理的鲁棒估计方法。第一种思路是采用加性对数比变换后的得分匹配估计，该估计量可自动规避数据成分中的零值问题；第二种思路是在估计方程中引入适当权重，使估计量额外具备对异常值的抗性。仿真研究验证了这些性质，同时进一步表明：即便在无模型污染的情况下，我们所提出的新型异常值鲁棒估计量在高浓度设定下仍具有高效性。文中以微生物组数据为例进行阐释，并附有用户友好的R语言配套软件包。