Symbolic data analysis
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In statistics, usually data are formatted as single values. However, sometimes the data are represented by lists, intervals, histograms or even distributions. To deal with these kinds of data, the concept of symbolic data was introduced by Diday (1987). Among symbolic data, interval-valued data are the most commonly seen in application. Recently, different approaches have been introduced to analyze interval-valued data, including linear regression, principal component analysis and clustering, etc. This research focuses on interval-valued data regression analyses. The study begins with the concept of symbolic data, definition of symbolic interval-valued data and its descriptive statistics, and existing linear regression approaches. It then proposes new approaches, including the symbolic covariance method and symbolic likelihood method with their algorithms and applications and shows the two methods obtain identical results under certain conditions. The proposed methods are applied to real data and simulated data along with other methods and their performances are discussed.