Coefficient Estimation and Hypothesis Testing on Interval-Valued Data Regression by Measurement Error

• Activity Number: 425 - SPEED: Reliable Statistical Learning and Data Science
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 3:05 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Yaotong Cai* and lynne Billard
• Companies: University of Georgia and University of Georgia
• Keywords: Symbolic Data ; Measurement Error ; Linear Regression ; Internal Variation

Abstract

Among different types of symbolic data, interval-valued data is one of the most common to be studied. Compared with several approaches of statistical inference on interval-valued linear regression model, measurement error theory provides a new perspective about how to estimate coefficient estimates as well as their variances. By means of measurement error, the constraint that values within interval observations follow a uniform distribution can be relaxed when conducting inference on interval-valued data. In this paper, we first introduce concepts of measurement error and then propose an approach of coefficient estimation and hypothesis testing by measurement error for regression models on interval-valued data, with several different distribution assumptions on the within values. The proposed method are applied to real data and simulated data with performances being discussed.