论文标题
柔性非参数回归模型的组成数据模型
Flexible non-parametric regression models for compositional data
论文作者
论文摘要
需要在许多现实生活应用程序和多功能方法中出现组成数据，以在回归上下文中正确分析此类数据。当参数假设无法保持或难以验证时，非参数回归模型可以为预测提供方便的替代方法。为此，我们考虑了经典$ k $ - $ nn $回归的扩展，称为$α$ - $ k $ - $ nn $回归，该回归通过使用$α$转换，得出了高度灵活的非参数回归模型，用于组成数据。与许多用于组成数据的建议回归模型不同，零值（通常在实践中发生）并非有问题，并且可以将其纳入建议的模型而无需修改。广泛的仿真研究和现实数据分析强调了使用这些非参数回归来对组成响应数据和欧几里得预测变量之间的复杂关系的优势。两者都表明，与当前的回归模型相比，$α$ - $ k $ - $ nn $回归可以导致更准确的预测，这些回归模型假定与预测变量有时，有时是限制性的参数关系。此外，与当前的回归技术相比，$α$ - $ k $ - $ nn $回归具有较高的计算效率，使其非常有吸引力，可用于大规模，大型或大数据。
Compositional data arise in many real-life applications and versatile methods for properly analyzing this type of data in the regression context are needed. When parametric assumptions do not hold or are difficult to verify, non-parametric regression models can provide a convenient alternative method for prediction. To this end, we consider an extension to the classical $k$--$NN$ regression, termed $α$--$k$--$NN$ regression, that yields a highly flexible non-parametric regression model for compositional data through the use of the $α$-transformation. Unlike many of the recommended regression models for compositional data, zeros values (which commonly occur in practice) are not problematic and they can be incorporated into the proposed models without modification. Extensive simulation studies and real-life data analyses highlight the advantage of using these non-parametric regressions for complex relationships between the compositional response data and Euclidean predictor variables. Both suggest that $α$--$k$--$NN$ regression can lead to more accurate predictions compared to current regression models which assume a, sometimes restrictive, parametric relationship with the predictor variables. In addition, the $α$--$k$--$NN$ regression, in contrast to current regression techniques, enjoys a high computational efficiency rendering it highly attractive for use with large scale, massive, or big data.
