Robust nonparametric inferences in longitudinal data and quality control

纵向数据和质量控制中的稳健非参数推理

• 批准号: 356148-2010
• 负责人: MulayathVariyath, Asokan
• 金额: $ 0.87万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=459760
• 关键词: Robust; nonparametric; inferences; longitudinal; data

In the statistical model building process, distributional assumptions of the random variable play a significant role in the statistical inference of the parameters. If the statistical models are not correctly specified, the validity of the conclusions becomes questionable. In this proposed research project, I propose a non-parametric modeling of data and use robust methods to estimate the parameters of interest. These proposed methods will help the scientific community to undertake their studies in a flexible way with more confidence in their assumptions. In the first project, I propose the modeling of longitudinal data based on empirical likelihood to make valid inference on the regression parameters. Empirical likelihood has properties similar to parametric likelihood and performs better in situations where the models are slightly deviated. Also empirical likelihood based confidence interval for the parameter has data driven shapes. I also propose a penalized empirical likelihood for variable selection. In this formulation, the estimation and variable selection will be carried out simultaneously. Moreover, the proposed penalized EL based variable selection can be used in any variable selection problem which increases its scope. In the second project, I propose three important practical problems in statistical process control. By the introduction of six sigma strategy for improving quality of product and services by leading industries worldwide, there is a need for robust multivariate techniques to control the process. My proposed methods which are applicable to any type of data will definitely help the quality professional to monitor and control the process in a more efficient way resulting in improved customer satisfaction in the long run. I propose an empirical likelihood based control chart for monitoring the process mean in an industrial set-up and identification of change points. There is no need for any distributional assumption in the construction of the empirical likelihood control charts. I propose to undertake a study on monitoring the correlated count data. Correlated count data will be modeled using an integer valued autoregressive model and the generalized quasi-likelihood method will be used to estimate the parameters.

在统计模型构建过程中，随机变量的分布假设对参数的统计推断起着重要作用。 如果统计模型没有正确指定，结论的有效性就会受到质疑。在这个拟议的研究项目中，我提出了一种数据的非参数建模，并使用稳健的方法来估计感兴趣的参数。这些提出的方法将帮助科学界以灵活的方式进行研究，并对他们的假设更有信心。在第一个项目中，我提出基于经验似然的纵向数据建模，以对回归参数做出有效的推断。经验似然具有与参数似然类似的属性，并且在模型略有偏差的情况下表现更好。 此外，参数的基于经验似然的置信区间具有数据驱动的形状。 我还提出了变量选择的惩罚经验可能性。在该公式中，估计和变量选择将同时进行。此外，所提出的基于惩罚 EL 的变量选择可以用于任何扩大其范围的变量选择问题。在第二个项目中，我提出了统计过程控制中的三个重要的实际问题。 通过引入六西格玛战略来提高全球领先行业的产品和服务质量，需要强大的多变量技术来控制流程。我提出的适用于任何类型数据的方法肯定会帮助质量专业人员以更有效的方式监视和控制流程，从而从长远来看提高客户满意度。我提出了一种基于经验似然的控制图，用于监控工业设置中的过程平均值并识别变化点。在构建经验似然控制图时不需要任何分布假设。我建议开展一项监测相关计数数据的研究。将使用整数值自回归模型对相关计数数据进行建模，并使用广义拟似然方法来估计参数。