Collaborative Research: Integral Transform Methods for Sufficient Dimension Reduction in Regression

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This project is aimed to develop theory and methods for sufficient dimension reduction in regression analysis involving a large number of predictor variables. The investigators propose a general approach called the integral transform approach to facilitating dimension reduction. The key idea of this approach is to use integral transform and response transformation to change the domain where dimension reduction is performed. Due to the availability of a wide range of transformations and integral transforms, this approach leads to a flexible and effective framework for addressing and resolving challenges raised by high dimensionality. Through a series of well-defined research problems, the investigators study this framework and develop specific dimension reduction methods for many important regression applications. The success of this project not only provides effective practical tools for high-dimensional data analysis but also represents an advance in the theory and methodology of semiparametric inference.High-dimensional data that involve a large amount of variables are nowadays routinely generated and collected in areas such as scientific research, government, business, etc. It is well-known that high dimensionality causes difficulties in processing and analyzing these data. This is commonly referred to as the curse of dimensionality. There is an urgent demand of statistical tools that are able to mitigate the curse of dimensionality through dimension reduction. This project represents an answer to this demand and is particularly aimed at achieving dimension reduction in regression. The results from this project can be widely applied in areas where regression involving a large number of variables is required. Gene expression and protein sequence data analysis is one such example. Therefore, this project can help enhance scientific research and discovery and benefit a variety of social and economical activities.