Robust Statistical Data Analysis and Modeling.

Abstract : The original proposal for this research project states its goals as follows: The object of this research project is to continue a broad program of research whose aims are: to develop the quantile and density-quantile function formulation of statistical data analysis and modeling problems; to develop robust methods of data analysis and modeling; to develop density estimation methods; and to develop minimum distance methods and approximation theory methods. The author proposes to implement our theoretical research in algorithms and computer software which provide methods useable by researchers concerned with important scientific and social problems, and to discuss applications which illustrate the applicability of the methods. The approach to statistical reasoning that our research program is attempting to develop has reached a synthesis that warrants its own name; we propose the name FUN.STAT. The FUN.STAT domain of statistical data model identification and parameter estimation combines (1) density-quantile function signatures of distributions, (2) entropy and information measures, and (3) functional statistical inference.