Robust nonparametric inferences in longitudinal data and quality control

在统计建模过程中，随机变量的分布假设对参数的统计推断起着重要作用。 如果统计模型没有被正确地指定，结论的有效性就成了问题。在这个拟议的研究项目中，我提出了一个数据的非参数建模，并使用强大的方法来估计感兴趣的参数。这些拟议的方法将有助于科学界以灵活的方式进行研究，对他们的假设更有信心。在第一个项目中，我提出了基于经验似然的纵向数据建模，对回归参数进行有效的推断。经验似然具有类似于参数似然的属性，并且在模型稍微偏离的情况下表现得更好。 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。 我还提出了一个惩罚的经验可能性变量选择。在该公式中，估计和变量选择将同时进行。此外，建议的惩罚EL基于变量选择可以用于任何变量选择问题，这增加了它的范围。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。 随着六西格玛战略的引入，全球领先的行业都在提高产品和服务的质量，这就需要稳健的多变量技术来控制过程。我提出的方法适用于任何类型的数据，肯定会帮助质量专业人员以更有效的方式监测和控制过程，从而提高客户的长期满意度。我提出了一个经验的可能性为基础的控制图，用于监测过程中的工业设置和识别的变化点。在构造经验似然控制图时，不需要任何分布假设。我建议进行一项研究，以监察相关的点票数据。将使用整数值自回归模型对相关计数数据进行建模，并使用广义准似然法估计参数。

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.