  Nonlinear expectation, including sublinear expectation as its special case,
is a new and original framework of probability theory and has potential
applications in some scientific fields, especially in finance risk measure and
management. Under the nonlinear expectation framework, however, the related
statistical models and statistical inferences have not yet been well
established. The goal of this paper is to construct the sublinear expectation
regression and investigate its statistical inference. First, a sublinear
expectation linear regression is defined and its identifiability is given.
Then, based on the representation theorem of sublinear expectation and the
newly defined model, several parameter estimations and model predictions are
suggested, the asymptotic normality of estimations and the mini-max property of
predictions are obtained. Furthermore, new methods are developed to realize
variable selection for high-dimensional model. Finally, simulation studies and
a real-life example are carried out to illustrate the new models and
methodologies. All notions and methodologies developed are essentially
different from classical ones and can be thought of as a foundation for general
nonlinear expectation statistics.
