Variable Selection for Global Fréchet Regression
针对响应变量为分布、网络等度量空间值的新型回归模型，提出了一种变量选择方法，并证明了其选择一致性，通过数值例子验证了有限样本性能。
Global Fréchet regression is an extension of linear regression to cover more general types of responses, such as distributions, networks, and manifolds, which are becoming more prevalent. In such models, predictors are Euclidean while responses are metric space valued. Predictor selection is of major relevance for regression modeling in the presence of multiple predictors but has not yet been addressed for Fréchet regression. Due to the metric space-valued nature of the responses, Fréchet regression models do not feature model parameters, and this lack of parameters makes it a major challenge to extend existing variable selection methods for linear regression to global Fréchet regression. In this work, we address this challenge and propose a novel variable selection method that overcomes it and has good practical performance. We provide theoretical support and demonstrate that the proposed variable selection method achieves selection consistency. We also explore the finite sample performance of the proposed method with numerical examples and data illustrations.