Model selection criteria are rules used to select the best statistical model among a set of candidate models, striking a trade-off between goodness of fit and model complexity. Most popular model selection criteria measure the goodness of fit trough the model log-likelihood function, yielding to non-robust criteria. This paper presents a new family of robust model selection criteria for independent but not identically distributed observations (i.n.i.d.o.) based on the R\'enyi's pseudodistance (RP). The RP-based model selection criterion is indexed with a tuning parameter $\alpha$ controlling the trade-off between efficiency and robustness. Some theoretical results about the RP criterion are derived and the theory is applied to the multiple linear regression model, obtaining explicit expressions of the model selection criterion. Moreover, restricted models are considered and explicit expressions under the multiple linear regression model with nested models are accordingly derived. Finally, a simulation study empirically illustrates the robustness advantage of the method.

翻译：模型选择准则是用于从一组候选模型中选取最优统计模型的规则，需在拟合优度与模型复杂度之间取得平衡。最常用的模型选择准则通过模型对数似然函数衡量拟合优度，导致其缺乏稳健性。本文针对独立但非同分布观测（i.n.i.d.o.）数据，提出一类基于Rényi伪距离（RP）的新型稳健模型选择准则族。该准则通过调整参数$\alpha$控制效率与稳健性之间的权衡。本文推导了RP准则的部分理论结果，并将其应用于多元线性回归模型，获得了模型选择准则的显式表达式。此外，考虑受限模型情形，并相应推导了嵌套模型下多元线性回归模型的显式表达式。最后，模拟研究通过实证展示了该方法的稳健性优势。