Lasso Estimation of an Interval-Valued Multiple Regression Model

TL;DR

This paper introduces a LASSO-based estimation method for an interval-valued multiple regression model, improving parameter selection by addressing cross-relationship irrelevance, and compares it with existing least-squares approaches.

Contribution

It develops a novel LASSO estimation approach for interval-valued regression models, enhancing model sparsity and interpretability over traditional least-squares methods.

Findings

LASSO estimator effectively selects relevant cross-relationships.

Comparative analysis shows differences between LASSO and least-squares estimators.

LASSO improves model simplicity and interpretability.

Abstract

A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried out by transforming a quadratic optimization problem with inequality constraints into a linear complementary problem and using Lemke's algorithm to solve it. Due to the irrelevance of certain cross-relationships, an alternative estimation process, the LASSO (Least Absolut Shrinkage and Selection Operator), is developed. A comparative study showing the differences between the proposed estimators is provided.