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Seemingly unrelated regression tree

机译：看似无关的回归树

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摘要

Nonparametric seemingly unrelated regression provides a powerful alternative to parametric seemingly unrelated regression for relaxing the linearity assumption. The existing methods are limited, particularly with sharp changes in the relationship between the predictor variables and the corresponding response variable. We propose a new nonparametric method for seemingly unrelated regression, which adopts a tree-structured regression framework, has satisfiable prediction accuracy and interpretability, no restriction on the inclusion of categorical variables, and is less vulnerable to the curse of dimensionality. Moreover, an important feature is constructing a unified tree-structured model for multivariate data, even though the predictor variables corresponding to the response variable are entirely different. This unified model can offer revelatory insights such as underlying economic meaning. We propose the key factors of tree-structured regression, which are an impurity function detecting complex nonlinear relationships between the predictor variables and the response variable, split rule selection with negligible selection bias, and tree size determination solving underfitting and overfitting problems. We demonstrate our proposed method using simulated data and illustrate it using data from the Korea stock exchange sector indices.
机译：非参数看似无关的回归为放松线性假设提供了一种强大的替代方法，可替代参数看似无关的回归。现有方法受到限制，特别是在预测变量与相应的响应变量之间的关系发生急剧变化的情况下。我们为看似无关的回归提出了一种新的非参数方法，该方法采用树结构回归框架，具有令人满意的预测准确性和可解释性，对包含类别变量没有限制，并且较不容易受到维度诅咒的影响。此外，一个重要的功能是为多变量数据构建统一的树结构模型，即使与响应变量相对应的预测变量完全不同。这种统一的模型可以提供启示性的见解，例如潜在的经济意义。我们提出了树结构回归的关键因素，即检测预测变量和响应变量之间复杂非线性关系的杂质函数，选择偏差可忽略的分裂规则选择以及解决过拟合和过拟合问题的树大小确定。我们使用模拟数据演示了我们提出的方法，并使用了韩国证券交易所行业指数的数据对其进行了说明。

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