发表机构
Sauder School of Business, University of British Columbia; Columbia University; Department of Statistics and Actuarial Science, Simon Fraser University（不列颠哥伦比亚大学 Sauder 商学院; 哥伦比亚大学; 西蒙菲莎大学统计与精算科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种面向多总体数据的半参数函数型广义线性模型，通过密度比模型关联多总体基线响应分布，采用最大经验似然估计与惩罚B样条近似，经模拟及大豆产量数据验证可提升估计效率且具稳健性。
AI 中文摘要
函数型广义线性模型提供了将标量响应与函数型及标量预测因子关联的灵活框架，但其传统形式需指定响应分布，且通常针对单一总体开发。本文提出一种面向多总体数据的半参数函数型广义线性模型，该模型不指定基线响应分布，而是通过密度比模型将各总体的基线响应分布关联起来。所提框架可同时适配函数型与标量预测因子，且能从相关总体间借用信息。本文开发了最大经验似然估计程序，并采用惩罚B样条近似来估计函数型系数；还引入了基于核平滑经验似然密度估计器的交叉验证程序以选择平滑参数。模拟研究表明，与单独拟合每个总体相比，通过密度比结构借用信息可提升估计效率；当参数高斯模型被正确指定时，所提半参数方法仍具竞争力，而当模型设定错误时则展现出显著的稳健性。本文使用来自堪萨斯州的县级大豆产量数据对该方法进行了说明，其中以每日温度曲线和灌溉水平作为预测因子。
英文摘要
Functional generalized linear models provide a flexible framework for relating a scalar response to functional and scalar predictors, but their conventional formulation requires specification of the response distribution and is typically developed for a single population. We propose a semiparametric functional generalized linear model for multi-population data that leaves the baseline response distributions unspecified and links them across populations through a density ratio model. The proposed framework accommodates both functional and scalar predictors while borrowing information across related populations. We develop a maximum empirical likelihood estimation procedure and use penalized B-spline approximations to estimate the functional coefficients. A cross-validation procedure based on a kernel-smoothed empirical likelihood density estimator is introduced to select the smoothing parameters. Simulation studies show that borrowing information through the density ratio structure can improve estimation efficiency relative to fitting each population separately, and that the proposed semiparametric method remains competitive when a parametric Gaussian model is correctly specified while providing substantial robustness when it is misspecified. We illustrate the method using county-level soybean yield data from Kansas, with daily temperature curves and irrigation levels as predictors.
