Empirical Process and Modern Statistical Decision Theory

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The workshop titled "Empirical Process and Modern Statistical Decision Theory" will be held at Yale University on May 7-9, 2015. The era of big data is fundamentally changing every aspect of our life through discoveries in science, medicine, and engineering. Many innovative and intuitively appealing methodologies have been proposed to make novel and significant discoveries by analysis of complex and big data. It is timely and critically important for statisticians to develop deep, broad, and formal statistical theory to understand and justify why and when certain methodologies would work or not work, to guide statistical practice to make valid and influential contributions to our society. This workshop will bring together some of authorities in statistical decision theory and empirical Process to review the most important and influential advances in the past, to report their most recent exciting research, and to discuss their view of future developments. The workshop will provide a venue for promising young researchers to interact with these leaders of the field and each other, leading to future collaborations and discoveries. A potential outcome of this workshop will provide a guidance to researchers and professors on how and what to teach in empirical process to train our students in understanding and developing modern statistical decision theory.Empirical process has been playing a key role in developing modern statistical decision theory for a wide range of important models and significant methodologies, such as providing a unified framework for many high dimensional linear models by Gaussian width, establishing asymptotic equivalence theory of Le Cam for various statistical models by the KMT construction, and justifying the effectiveness of important algorithms in machine learning including SVM by VC dimension. In the last ten to fifteen years, the statistics research has witnessed a tremendous successes of empirical process theory in Bayesian nonparametrics, shape constrained estimation, robust estimation, minimax regret, lasso, and sparse principal component analysis. This workshop will bring together some of authorities in statistical decision theory including Lawrence Brown and Iain Johnstone, and in empirical processes including Richard Dudley and Evarist Gine, as well as some of the the most prominent researchers in high dimensional estimation, Bayesian nonparametrics, robust estimation, machine learning, and shape constrained estimation, to celebrate the most significant advances in the past and to discuss exciting future developments.