发表机构
Fırat University（菲拉特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出洛伦兹双曲加权回归，用双曲空间距离定义局部性，理论分析一致性等，模拟与141国GDP预测显示优于全局与地理加权回归。
AI 中文摘要
许多应用为每个观测值提供了有意义的表示，以及普通的响应和协变量。当该表示是层次结构、枢纽-外围结构或网络衍生时，欧几里得或地理邻近性可能定义错误的同行群体。我们提出洛伦兹双曲加权回归（LHWR）作为该设置下的一种实用局部回归方法。响应和预测变量保持实值；仅局部性由在洛伦兹双曲空间模型上表示的观测值之间的距离定义。我们描述了坐标构建、自适应带宽选择、预测、局部系数汇总、共线性检查和残差自相关诊断。理论结果解释了一致性、偏差-方差权衡、曲率效应以及由估计表示引起的额外不确定性。模拟表明，洛伦兹几何对于急剧局部化的系数表面最有用，而切平面近似对于平滑表面可能具有竞争力。在141个国家的世界发展指标示例中，基于收入和贸易开放度的经济相似性定义了局部同行群体。基于表示的局部性在预测GDP增长方面优于全局最小二乘和地理加权回归，尽管洛伦兹、庞加莱和切线度量之间的差异不大。主要的实际教训是，表示应科学选择，距离几何应检查而非假设。
英文摘要
Many applications provide each observation with a meaningful representation in addition to an ordinary response and covariates. When that representation is hierarchical, hub-periphery structured, or network derived, Euclidean or geographic proximity may define the wrong peer groups. We present Lorentz hyperbolic weighted regression (LHWR) as a practical local regression method for this setting. Responses and predictors remain real valued; only locality is defined by distances between observations represented on the Lorentz model of hyperbolic space. We describe coordinate construction, adaptive bandwidth selection, prediction, local coefficient summaries, collinearity checks, and residual autocorrelation diagnostics. Theoretical results explain consistency, bias-variance tradeoffs, curvature effects, and the extra uncertainty caused by estimated representations. Simulations show that the Lorentz geometry is most useful for sharply localized coefficient surfaces, whereas tangent-plane approximations can be competitive for smooth surfaces. In a 141-country World Development Indicators illustration, economic similarity based on income and trade openness defines local peer groups. Representation-based locality predicts GDP growth better than global least squares and geographically weighted regression, although differences among Lorentz, Poincare, and tangent metrics are modest. The main practical lesson is that the representation should be chosen scientifically and the distance geometry should be checked rather than assumed.
Comments42 pages; integrated technical appendices; R package: https://github.com/byuzbasi/LHWL
