数据缺失下的HIV感染率预测:基于函数型数据分析方法

doi:10.6040/j.issn.1671-9352.0.2025.053

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (9): 56-63.doi: 10.6040/j.issn.1671-9352.0.2025.053

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数据缺失下的HIV感染率预测:基于函数型数据分析方法

彭倩倩,凌能祥^*

合肥工业大学数学学院, 安徽合肥 230009

发布日期:2026-09-30
通讯作者: 凌能祥(1964— ),男,教授,博士生导师,研究方向为函数型数据分析、非参数统计. E-mail:hfut.lnx@163.com
作者简介:彭倩倩(2000— ),女,硕士研究生,研究方向为概率论与数理统计. E-mail:pqq101113@163.com*通信作者:凌能祥(1964— ),男,教授,博士生导师,研究方向为函数型数据分析、非参数统计. E-mail:hfut.lnx@163.com
基金资助:
国家自然科学基金资助项目(72071068)

Prediction of HIV infection rates with missing data: based on a functional data analysis approach

PENG Qianqian, LING Nengxiang^*

School of Mathematics, Hefei University of Technology, Hefei 230009, Anhui, China

Published:2026-09-30

摘要/Abstract

摘要： 针对人类免疫缺陷病毒(human immunodeficiency virus, HIV)感染率的预测问题,构建部分函数型线性分位数回归模型。该模型突破传统均值回归局限,能够刻画不同指标对HIV感染率的影响特征。对于实际数据中函数型解释变量与数值响应变量同时缺失的复杂情况,提出融合函数型数据重构与回归插补的联合处理方法。此外,将该方法与其他常用曲线重构和数据插补方法进行比较,结果表明,所提方法在处理数据缺失和提高预测精度方面具有优势。

关键词: 函数型数据, 部分线性分位数回归模型, HIV感染率, 数据缺失

Abstract: A partial functional linear quantile regression model is constructed to address the prediction of human immunodeficiency virus(HIV)infection rates. The model overcomes the limitations of traditional mean regression and captures the influence characteristics of different indicators on HIV infection rates. For the complex scenario where both functional explanatory variable and scalar response variable are missing in real-world data, a joint processing method integrating functional data reconstruction and regression imputation is proposed. Additionally, the proposed method is compared with other commonly used curve reconstruction and data imputation approaches. The results demonstrate that the proposed method exhibits advantages in handling missing data and improving prediction accuracy.

Key words: functional data, partial linear quantile regression model, HIV infection rate, missing data

中图分类号:

O212

彭倩倩,凌能祥. 数据缺失下的HIV感染率预测:基于函数型数据分析方法[J]. 《山东大学学报(理学版)》, 2026, 61(9): 56-63.

PENG Qianqian, LING Nengxiang. Prediction of HIV infection rates with missing data: based on a functional data analysis approach[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(9): 56-63.

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数据缺失下的HIV感染率预测:基于函数型数据分析方法

Prediction of HIV infection rates with missing data: based on a functional data analysis approach

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