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Abstract:
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Interval-valued data is one of the most common forms of symbolic data. Previous studies have provided a number of approaches to conducting linear regression models for interval data, while few have involved issues surrounding inference on the regression coefficient estimates. In this paper, we first introduce the concept of measurement error in the interpretations of interval-valued data, and then propose a process of hypothesis testing on coefficient estimates for linear regression by means of utilizing instrument variables in measurement error theory. The proposed method is applied to real data and simulated data and the performances are discussed.
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