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MLE for the parameters of bivariate interval-valued model

Author

Listed:
  • S. Yaser Samadi

    (Southern Illinois University)

  • L. Billard

    (University of Georgia)

  • Jiin-Huarng Guo

    (National Pingtung University)

  • Wei Xu

    (Capital One)

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.

Suggested Citation

  • S. Yaser Samadi & L. Billard & Jiin-Huarng Guo & Wei Xu, 2024. "MLE for the parameters of bivariate interval-valued model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(4), pages 827-850, December.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:4:d:10.1007_s11634-023-00546-6
    DOI: 10.1007/s11634-023-00546-6
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    References listed on IDEAS

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    1. Samadi, S. Yaser & Billard, Lynne, 2021. "Analysis of dependent data aggregated into intervals," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    2. Fei Liu & L. Billard, 2022. "Partition of Interval-Valued Observations Using Regression," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 55-77, March.
    3. M. Rosário Oliveira & Margarida Azeitona & António Pacheco & Rui Valadas, 2022. "Association measures for interval variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 491-520, September.
    4. D. G. Malcolm & J. H. Roseboom & C. E. Clark & W. Fazar, 1959. "Application of a Technique for Research and Development Program Evaluation," Operations Research, INFORMS, vol. 7(5), pages 646-669, October.
    5. Charles E. Clark, 1962. "Letter to the Editor---The PERT Model for the Distribution of an Activity Time," Operations Research, INFORMS, vol. 10(3), pages 405-406, June.
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