A fuzzy regression approach using Bernstein polynomials for the spreads: Computational aspects and applications to economic models

An important research topic in applied statistics consists of determining the relationship between several variables through a regression function. Recently, fuzzy regression analysis has become important to deal with fuzzy data and vague information captured from the real world. When we are modeling relationships between an imprecise response and several real exploratory variables, one of the main difficulties is to guarantee the condition of non-negativity of the spreads. In this paper, due to their ease of implementation, continuous differentiability, and theoretical properties, Bernstein polynomials are used to develop a fuzzy regression procedure which guarantees this condition. We demonstrate the applicability and effectiveness of our method through the analysis of real data and comparisons with existing methodologies.