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Modern statistics is faced with a series of challenges as it addresses an expanding number of applications in machine learning, artificial intelligence, forecasting, cyber security, smart systems, social networks, and developing the internet of things. The challenges derive from the large-scale nature of these applications, presence of multi-attribute data of varying and unknown quality and relevance, nonstationarity of the arriving information, and multi-stage nature of the problems.
Optimization theories and algorithms have supported classical statistics well for decades as prominently illustrated by the deep understanding and wide application of regression models, likelihood maximization, and more generally M-estimators. These theories and algorithms, together with those of linear algebra and calculus of variations, have played an essential part in the development of rigorous and efficient statistical procedures that consistently provide users with reliable results. However, the...