Time Series and Spectral Methods for Imputation, Regression, and Environmental Health

用于插补、回归和环境健康的时间序列和谱方法

• 批准号: RGPIN-2017-04741
• 负责人: Burr, Wesley
• 金额: $ 1.02万
• 依托单位: Trent University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=646579
• 关键词: Time; Series; Spectral; Methods; Imputation

Progress in statistical methods is vital for making sense of an ever-increasing flow of data. Time series are a type of data consisting of repeated observations of a physical phenomena, indexed by a common factor. The proposed research deals with the reconstruction of missing samples in such time series, the estimation of the spectra of them, and the use of both in regression models. The research falls within two distinct statistical areas, both dealing with data: the first in the pre-analysis stage (interpolating raw time series), and the second in the analysis stage (development of models for analysis).***The analysis of time series in the natural sciences is a key element in the interpretation of real-world phenomena. These analyses have increasing value and predictive power as the length of the data series increases. Unfortunately, such series are often plagued by missing records. Interpolation allows for the reconstruction of values for missing records, extending the inferential power of the overall series. One prong of the proposed research centres on the development of algorithms and theory for the interpolation of time series. The challenge with such algorithms is the complex nature of real-world time series, and developing models which allow for violations of simplistic assumptions is the primary objective of the research. ***The proposed research on model development consists of application of time series spectral methods to two problems: the estimation of limited timescale associations in additive models, and the estimation of lagged associations. The first of these is a problem of mixed data, with both predictor and response having elements driven by long-term effects (e.g., mortality records vary annually), but with the inference desired being that of the short-term effects: careful work is required to separate the two. The second of these problems is that of delayed effects, where predictors have time delayed associations with responses. The research proposed develops a novel modelling framework for estimation of these delayed effects, eliminating an identifiability issue of previous solutions.***The work proposed here will address these problems relating to time series data, and lead to original research that will further the scientific use of complex time series. The work on time series interpolation will be of value to researchers seeking to analyze long time series, while the work on additive models will be of value to researchers for whom these models are a primary working tool for estimation of timescale-limited associations. A further impact will be to refine and improve the reliability of risk estimation for population health, which ultimately will affect the policies made by our government that pertain to the health of Canadians. Training is a major component of this research program, which will support 1 Phd and 7 MSc graduate students, as well as 8 undergraduate summer research students.

统计方法的进步对于理解不断增长的数据流至关重要。时间序列是一种由物理现象的重复观测组成的数据类型，由公共因子索引。建议的研究涉及重建丢失的样本在这样的时间序列，估计的频谱，并使用两者的回归模型。研究福尔斯属于两个不同的统计领域，都处理数据：第一个在预分析阶段（内插原始时间序列），第二个在分析阶段（开发分析模型）。自然科学中的时间序列分析是解释现实世界现象的关键因素。随着数据系列长度的增加，这些分析具有越来越大的价值和预测能力。不幸的是，这样的系列经常被缺失的记录所困扰。插值允许重建缺失记录的值，扩展整个系列的推理能力。拟议的研究重点之一是发展时间序列内插的算法和理论。这种算法的挑战是现实世界时间序列的复杂性，开发允许违反简单假设的模型是研究的主要目标。* 关于模型开发的拟议研究包括将时间序列谱方法应用于两个问题：加性模型中有限时间尺度关联的估计和滞后关联的估计。其中第一个是混合数据的问题，预测因子和响应都具有由长期效应驱动的元素（例如，死亡率记录每年都有变化），但所需的推断是短期影响：需要仔细工作将两者分开。这些问题中的第二个是延迟效应，其中预测因子与响应具有时间延迟关联。这项研究提出了一种新的建模框架，用于估计这些延迟效应，消除了以前解决方案的可识别性问题。这里提出的工作将解决与时间序列数据有关的这些问题，并导致原始研究，这将进一步科学地利用复杂的时间序列。时间序列插值的工作将是有价值的研究人员寻求分析长时间序列，而添加剂模型的工作将是有价值的研究人员，对他们来说，这些模型是一个主要的工作工具，用于估计的时间尺度有限的协会。进一步的影响将是完善和提高人口健康风险估计的可靠性，这最终将影响我国政府制定的与加拿大人健康有关的政策。培训是该研究计划的主要组成部分，将支持1名博士和7名硕士研究生，以及8名本科夏季研究生。