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Interpoint distance tests for high-dimensional comparison studies

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  • Marco Marozzi
  • Amitava Mukherjee
  • Jan Kalina

Abstract

Modern data collection techniques allow to analyze a very large number of endpoints. In biomedical research, for example, expressions of thousands of genes are commonly measured only on a small number of subjects. In these situations, traditional methods for comparison studies are not applicable. Moreover, the assumption of normal distribution is often questionable for high-dimensional data, and some variables may be at the same time highly correlated with others. Hypothesis tests based on interpoint distances are very appealing for studies involving the comparison of means, because they do not assume data to come from normally distributed populations and comprise tests that are distribution free, unbiased, consistent, and computationally feasible, even if the number of endpoints is much larger than the number of subjects. New tests based on interpoint distances are proposed for multivariate studies involving simultaneous comparison of means and variability, or the whole distribution shapes. The tests are shown to perform well in terms of power, when the endpoints have complex dependence relations, such as in genomic and metabolomic studies. A practical application to a genetic cardiovascular case-control study is discussed.

Suggested Citation

  • Marco Marozzi & Amitava Mukherjee & Jan Kalina, 2020. "Interpoint distance tests for high-dimensional comparison studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(4), pages 653-665, March.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:4:p:653-665
    DOI: 10.1080/02664763.2019.1649374
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    Cited by:

    1. Qiu, Tao & Xu, Wangli & Zhu, Liping, 2021. "Two-sample test in high dimensions through random selection," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    2. Modarres, Reza, 2022. "A high dimensional dissimilarity measure," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    3. Jan Kalina & Jan Tichavský, 2022. "The minimum weighted covariance determinant estimator for high-dimensional data," 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(4), pages 977-999, December.
    4. Modarres, Reza, 2023. "Analysis of distance matrices," Statistics & Probability Letters, Elsevier, vol. 193(C).

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