My Research Field
My research background spans M.S. degrees in mathematics and a Ph.D. degree in statistics. My interests have always been in the mathematical sciences, where my primary interest has been in solving real application problems using theory-driven scientific computation. My doctoral studies at the Auburn University have exposed me to interesting research topics in statistics and nurtured my interest in research.
My primary research interests are in robust statistical methods for functional data analysis. In particular, my dissertation work involves research on robust variable selection in functional linear regression model.
Interest in the area of robust statistics was borne at the Auburn University, where I was exposed to its importance. Robust statistics is a branch of statistics that deals with methodologies which are robust in nature to the outliers. Outliers play important role in revealing the true picture of the data and thus cannot be simply removed from the data to carry data analysis. The non-robust statistical methods fail in the presence of outliers, that's when robust statistics come into play.
Interest in the area of functional data was stimulated when I attended a course in fMRI data analysis at the Auburn University. The course focused on analysis of functional Magnetic Resonance Imaging (fMRI) of brain, which are functional data. Functional data are data that have been sampled discretely over a continuum, usually time with the assumption of underlying curve describing the data. Such data are very typical in various fields such as:
The analysis of brain imaging was an insightful event into how statistical methods could be integrated with fMRI studies. With the advancement of functional brain imaging techniques in recent years, the study of the relationship between brain and mind over time has led to an increased interest in developing statistical methods to work with functional data.
There are a wide variety of tools that are useful in analyzing functional brain images. The issues involved include problems of dimension reduction and important variable selection (feature selection) in functional magnetic resonance imaging data. It was with this in mind that I was drawn to work with the functional linear regression model that models functional predictors with a scalar response.
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