On the Estimation of the Regression Model M for Interval Data

Abstract

A linear regression model for interval data based on the natural interval-arithmetic has recently been proposed. Interval data can be identified with 2-dimensional points in ℝ × ℝ⁺, since they can be parametrized by its mid-point and its semi-amplitude or spread, which is non-negative. The model accounts separately for the contribution of the mid-points and the spreads through a single equation. The least squares estimation becomes a quadratic optimization problem subject to linear constraints, which guarantee the existence of the residuals. Several estimators are discussed. Namely, a closed-form estimator, the restricted least-squares estimator, an empirical estimator and an estimator based on separate models for mids and spreads have been investigated. Real-life examples are considered. Simulations are performed in order to assess the consistency and the bias of the estimators. Results indicate that the numerical and the closed-form estimator are appropriate in most of cases, while the empirical estimator and the one based on separate models are not always suitable.