MLE for the parameters of bivariate interval-valued model

S. Yaser Samadi (), L. Billard, Jiin-Huarng Guo and Wei Xu
Additional contact information
S. Yaser Samadi: Southern Illinois University
L. Billard: University of Georgia
Jiin-Huarng Guo: National Pingtung University
Wei Xu: Capital One

Advances in Data Analysis and Classification, 2024, vol. 18, issue 4, No 2, 827-850

Abstract: Abstract With contemporary data sets becoming too large to analyze the data directly, various forms of aggregated data are becoming common. The original individual data are points, but after aggregation the observations are interval-valued (e.g.). While some researchers simply analyze the set of averages of the observations by aggregated class, it is easily established that approach ignores much of the information in the original data set. The initial theoretical work for interval-valued data was that of Le-Rademacher and Billard (J Stat Plan Infer 141:1593–1602, 2011), but those results were limited to estimation of the mean and variance of a single variable only. This article seeks to redress the limitation of their work by deriving the maximum likelihood estimator for the all important covariance statistic, a basic requirement for numerous methodologies, such as regression, principal components, and canonical analyses. Asymptotic properties of the proposed estimators are established. The Le-Rademacher and Billard results emerge as special cases of our wider derivations.

Keywords: Interval data; Likelihood; Bivariate normal distribution; Bivariate Wishart distribution; Conditional moments; 62F10; 62F12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11634-023-00546-6

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