General Results on Strong Laws for Weighted Sums Under Sub-linear Expectations with a Statistical Application

Abstract

In this paper, the authors investigate the double-indexed version of the strong law of large numbers under some general conditions in a sub-linear expectation space. The weighted version of the Marcinkiewicz-Zygmund type strong law of large numbers is also established. These results extend or improve some existing ones in the classical probability space or a sub-linear expectation space. As an application, they further study the nonparametric regression model under the sub-linear expectation framework. Some numerical simulations are also presented.

Keywords

Strong law of large numbers / Sub-linear expectations / Nonparametric regression / Numerical simulation / 60F15 / 62G05

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