B-spline random functions and their forecast applications

Abstract

In this paper we introduce the concept of B-spline random function with empirical samples of two-dimensional random variables (X, Y) and prove that this random function better reflects the relationship between X and Y in case the correlation coefficient  is small, to prove this, we have introduced and proven the theorem (2.4). In the application, we have used the theorem (2.4) to establish a B-spline regression function for forecast.

Keywords: B-spline random function, B-spline regression function, correlation coefficient, empirical samples, random variable.