Recently, there has been significant interest in distribution-free prediction within the fields of machine learning and statistics. Distribution-free prediction involves techniques that aim to make predictions or create prediction intervals without relying on explicit assumptions about the underlying distribution of the data. In this study, we introduce an inductive conformal prediction strategy specifically designed for spatio-functional data. We define a prediction with a conformity level for the response of two distinct regression models: a Geographically Weighted Functional Regression model and its heteroscedastic version. We propose two novel measures of non-conformity and prediction bands for the functional response variable. The properties of the resulting estimates are examined through simulation and real data analysis on air quality data.

最近，机器学习和统计学领域对无分布预测产生了浓厚的兴趣。无分布预测涉及旨在进行预测或创建预测区间而不依赖于数据底层分布的显式假设的技术。在本研究中，我们引入了一种专为空间功能数据设计的归纳共形预测策略。我们为两个不同回归模型的响应定义了具有一致性水平的预测：地理加权函数回归模型及其异方差版本。我们提出了两种新颖的不合格测量方法和功能响应变量的预测带。通过对空气质量数据进行模拟和真实数据分析来检查所得估计值的特性。