k-sample upper expectation linear regression-Modeling, identifiability, estimation and prediction

Although nonlinear expectation theory has attracted much attention in literature, the related statistical models and statistical inferences have not yet been well established. The goal of this paper is to construct a k-sample upper expectation regression, a special nonlinear expectation regression, and then investigate its statistical properties. First, under the framework of k-sample, the upper expectation linear regression is defined and its identifiability is given. Then, based on the newly defined model together with k-sample, several estimations and predictions are suggested, consistency and asymptotic normality are established. Finally, simulation studies and a real financial example are carried out to illustrate the new methodology. All notions and methodologies developed are essentially different from classical ones and can be thought of as a foundation for general nonlinear expectation statistics.