Symbolic Interval-Valued Regression Model

Abstract

Symbolic data analysis can provide statistical inferences in macro-scale data while preserving as much information as possible from micro-scale data. In this study, we focus on the symbolic interval-valued regression model. The micro-scale data are reorganized into intervals by using the largest and smallest order statistics. Afterward, we develop innovative symbolic interval-valued regression models to construct the relationship between two or more intervals. By defining the negative sign for the intervals, we maintain the natural order in which the higher value of the dependent variable is larger than the lower value of the dependent variable, even when the values are negative. First, we develop a simple linear symbolic interval-valued regression model and derive the corresponding maximum likelihood estimators (MLEs). In addition, we describe the Fisher information matrix of the MLEs and show that they demonstrate asymptotic normality. Next, we extend the aforementioned model to a multiple linear symbolic interval-valued regression model, and the corresponding MLEs are again derived. Monte Carlo simulations and real data analysis confirm the validity of the proposed method.

Keywords: asynchronous observations; order statistics; regression; symbolic data analysis.

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