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Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
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Distance-Based Analysis with Quantile Regression Models.

Shaoyu Li1, Yanqing Sun1, Liyang Diao2

  • 1Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, USA.

Statistics in Biosciences
|July 18, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a linear quantile regression model for analyzing pairwise distances in complex, multivariate data. The method demonstrates reliable statistical properties for association studies, including microbiome analysis.

Keywords:
Asymptotic propertyEcologyMicrobiome association studyPairwise distanceQuantile regression

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Area of Science:

  • Multivariate statistics
  • Bioinformatics
  • Genomics
  • Ecology
  • Social Science

Background:

  • Emergence of non-standard structured, multivariate data across diverse research fields.
  • Prevalence of distance-based analyses utilizing pairwise distance measures for variable association.
  • Need for robust statistical methods to handle complex data structures.

Purpose of the Study:

  • To develop and analyze a linear quantile regression model specifically for pairwise distances.
  • To investigate the asymptotic properties of a novel coefficient estimator.
  • To establish statistical inference procedures for the proposed model.

Main Methods:

  • Formulation of a linear quantile regression model for pairwise distance data.
  • Theoretical investigation of large sample properties for the coefficient estimator.
  • Development of statistical inference techniques based on the estimator.

Main Results:

  • The proposed method exhibits satisfactory finite sample properties, as confirmed by extensive simulations.
  • The statistical inference procedures are validated through simulation studies.
  • The model's practical utility is demonstrated via application to a microbiome association study.

Conclusions:

  • The linear quantile regression model for pairwise distances provides a robust tool for association studies.
  • The developed statistical inference procedures are reliable for analyzing complex multivariate data.
  • The method offers a valuable approach for fields like genomics and microbiome research.