The investigator proposes to develop a new unified definition of multivariate skewed distributions, which are essential to statistical modeling of data. Indeed, skewed distributions provide flexible parametric classes of multivariate distributions for the statistician's toolkit that allow for modeling key characteristics such as skewness, heavy tails, and multimodality. They also contain the multivariate normal distribution as a special case, enjoy pleasant theoretical properties, and prevent the difficult task of multivariate data transformation. The investigator proposes to establish links between the new unified definition and existing definitions in the literature, as well as investigate novel distributions emerging from this framework. The investigator also intends to establish the theoretical and inferential properties of the multivariate skewed distributions resulting from the unified definition. This, in turn, provides the necessary basis for the development of selection models for spatial data, and yields a skewed version of the famed kriging procedure, or from another point of view, a spatial version of the celebrated Heckman model.
The primary impact of this project is that the new framework for multivariate skewed distributions will provide valuable tools to applied statisticians and practitioners, especially in environmental sciences. Another impact will result from the development and free distribution of implementations of the results emerging from this research in software such as R and Matlab. In order to facilitate the wide dissemination of results from this project, a webpage will be created and maintained. It will contain programs, research reports, references, and links to information about multivariate skewed distributions.
