Robust nonparametric inferences in longitudinal data and quality control

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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.