预测死亡率：用PCA-GEE方法揭示模式
Forecasting Mortality Rates: Unveiling Patterns with a PCA-GEE Approach
AI总结：
本文提出将PCA第一主成分作为协变量与GEE结合，用于单人口和多人口年龄别死亡率预测，并在多种相关结构下验证其优于Li-Lee和Lee-Carter模型的预测性能。
摘要：
主成分分析（PCA）是一种广泛应用于探索性数据分析、可视化和数据预处理的技术，它利用方差的概念来识别数据集中的关键维度。在本研究中，我们聚焦于第一主成分，它表示使投影数据方差最大化的方向。我们扩展了PCA的应用，将其第一主成分作为协变量，并与广义估计方程（GEE）相结合，用于分析纵向数据集中的年龄别死亡率（ASDRs）。选择GEE模型是因为其在处理相关数据方面具有稳健性，特别适用于传统模型假设观测之间相互独立、但在纵向数据中该假设可能不成立的情形。我们提出了针对单人口和多人口ASDRs量身定制的不同GEE模型，能够适应独立、AR(1)和可交换等多种相关结构，从而对模型效率进行全面评估。我们的研究通过详细的模型设定和实际示例，批判性地评估了GEE模型在死亡率预测中的优势与局限，并提供了实证证据。我们将PCA-GEE方法的预测准确性与Li-Lee和Lee-Carter模型进行了比较，证明了其更优的预测性能。我们的发现有助于更深入地理解GEE模型在死亡率预测中的细微能力，凸显了将PCA与GEE相结合以提高预测准确性和可靠性的潜力。
英文摘要：
Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the first principal component, which represents the direction maximizing the variance of projected data. We extend the application of PCA by treating its first principal component as a covariate and integrating it with Generalized Estimating Equations (GEE) for analyzing age-specific death rates (ASDRs) in longitudinal datasets. GEE models are chosen for their robustness in handling correlated data, particularly suited for situations where traditional models assume independence among observations, which may not hold true in longitudinal data. We propose distinct GEE models tailored for single and multipopulation ASDRs, accommodating various correlation structures such as independence, AR(1), and exchangeable, thus offering a comprehensive evaluation of model efficiency. Our study critically evaluates the strengths and limitations of GEE models in mortality forecasting, providing empirical evidence through detailed model specifications and practical illustrations. We compare the forecast accuracy of our PCA-GEE approach with the Li-Lee and Lee-Carter models, demonstrating its superior predictive performance. Our findings contribute to an enhanced understanding of the nuanced capabilities of GEE models in mortality rate prediction, highlighting the potential of integrating PCA with GEE for improved forecasting accuracy and reliability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
