Semiparametric Inference for Integer-Valued Time Series

整数值时间序列的半参数推理

• 批准号: RGPIN-2015-03889
• 负责人: Ghahramani, Melody
• 金额: $ 0.8万
• 依托单位: University of Winnipeg
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=708066
• 关键词: Semiparametric; Inference; Integer; Valued; Time

Discrete time series appear in a wide variety of settings. Energy forecasters may wish to understand patterns in the average number of windy days per month over time as a means to predicting wind power. Hydrologists may wish to forecast future river crests based on estimates of average number of rainy days. Public health officials may want to assess whether there is a declining trend in the number of cases of influenza over time after a major medical intervention such as mass immunizations.  One objective of statistical modeling of the dynamics of a time series is to predict future values of the series. Forecasting of river crests based on estimates of mean number of rainy days is an example of the latter objective. Yet another objective is to understand the relationship between typical values of the time series and a set of explanatory variables while adjusting for the dependent nature of the data. Estimating the trend in the average number of cases of a disease after an intervention is an example of the former objective; this approach is known as regression modeling. This research program is primarily concerned with time series regression modeling for discrete data. Usual time series regression modeling problems are studied as well as regression problems pertaining to "big data". When a large number of predictors are collected, not all variables will be fully relevant in explaining the mean counts. I will examine a "big data" technique known as "shrinkage estimation" that incorporates information from variables with partial relevance with a view towards improving prediction power of the regression model. Typical statistical models for count time series data make assumptions about the data generating mechanism giving rise to the data; these assumptions are in practice difficult to verify. In my research program, I relax assumptions about how discrete-valued time series data arise and study the advantages as well as the disadvantages from such a regression modeling approach. I adopt an estimating function theory modeling framework for model parameter estimation as it provides a unifying approach to discrete-valued time series estimation. The estimating function theory framework encompasses many of the statistical models proposed for explaining the dynamics for integer-valued time series. Furthermore, the methodology is easy to implement in contrast to some of the methods that require more stringent assumptions about the data generating mechanism. The findings from this research program will allow researchers to compare and contrast estimates derived from both the less restrictive methodology with that of existing methodology. If the results from both methodologies are very different, then the end users of the methodology will be able to use the results from this research program as an endpoint with confidence in their statistical conclusions.

离散时间序列出现在各种各样的设置。能源预报员可能希望了解每月平均大风天数随时间变化的模式，作为预测风力的一种手段。水文学家可能希望根据对平均雨天数的估计来预测未来的洪峰。公共卫生官员可能希望评估在大规模免疫接种等重大医疗干预后，流感病例数量是否随时间推移而呈下降趋势。 时间序列动态的统计建模的一个目标是预测序列的未来值。根据平均降雨天数的估计来预测河流洪峰是后一个目标的一个例子。另一个目标是了解时间序列的典型值和一组解释变量之间的关系，同时调整数据的相关性。估计干预后疾病平均病例数的趋势是前一个目标的一个例子;这种方法被称为回归建模。该研究计划主要关注离散数据的时间序列回归建模。研究了时间序列回归建模问题以及与“大数据”相关的回归问题。当收集大量预测因子时，并非所有变量都与解释平均计数完全相关。我将研究一种被称为“收缩估计”的“大数据”技术，该技术结合了部分相关变量的信息，旨在提高回归模型的预测能力。 计数时间序列数据的典型统计模型对产生数据的数据生成机制做出假设;这些假设在实践中难以验证。在我的研究项目中，我放松了对离散值时间序列数据如何产生的假设，并研究了这种回归建模方法的优点和缺点。我采用了估计函数理论建模框架模型参数估计，因为它提供了一个统一的方法来离散值时间序列估计。估计函数理论框架包括许多为解释整数值时间序列的动态而提出的统计模型。此外，该方法是很容易实现的一些方法，需要更严格的假设的数据生成机制相比。这项研究计划的结果将使研究人员能够比较和对比从限制较少的方法和现有方法得出的估计。如果两种方法的结果非常不同，则该方法的最终用户将能够使用本研究项目的结果作为终点，并对其统计结论充满信心。