Inferential studies for a flexible linear regression model for interval-valued variables

Abstract

Inferential studies for the regression coefficients of a linear model for interval-valued random variables are addressed. Confidence sets and hypothesis tests are investigated and solved through asymptotic and bootstrap techniques. The inferences are based on the least-squares estimators of the model which have been shown to be coherent with the interval arithmetic defining the model and to verify good statistical properties. Theoretical results assure the validity of the procedures. Moreover, some simulation studies and examples are considered to show the empirical behaviour and the practical applicability of the inferences.

Keywords:

• bootstrap
• inferences
• interval data
• linear regression
• set arithmetic

2010 AMS Subject Classifications:

• 62J05
• 62A86
• 62J86

Acknowledgments

Authors wish to thank the referees and the associate editor handling the manuscript for their very helpful suggestions and comments to improve the work. The research has been partially supported by the Spanish Government Grant MTM2013-44212-P and by the Principality of Asturias through SV-PA-13-ECOEMP-66 Grant. Their financial support is gratefully acknowledged.