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Quantile modeling through multivariate log-normal/independent linear regression models with application to newborn

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Summary
This summary is machine-generated.

This study introduces robust multivariate log-normal/independent distributions and linear regression models for skewed, heavy-tailed positive data. These models offer improved statistical modeling and parameter estimation using expectation-maximization algorithms.

Keywords:
EM algorithmmultivariate linear regressionmultivariate normal/independent distributionnewbornquantile modeling

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Robust Statistics

Background:

  • Correlated multivariate positive data often exhibit skewness and heavy tails, posing challenges for traditional statistical models.
  • Existing methods may lack robustness or flexibility in handling such complex data structures.

Purpose of the Study:

  • To propose and investigate a new class of multivariate log-normal/independent distributions.
  • To develop linear regression models based on this distribution class for robust statistical analysis.
  • To facilitate maximum likelihood estimation using expectation-maximization (EM)-type algorithms.

Main Methods:

  • Modeling relationships between response variable quantiles and explanatory variables.
  • Utilizing expectation-maximization (EM)-type algorithms for maximum likelihood estimation of model parameters.
  • Evaluating model performance using Mahalanobis-type distances and simulation studies.

Main Results:

  • The proposed multivariate log-normal/independent distributions are suitable for modeling skewed and heavy-tailed positive data.
  • EM-type algorithms provide efficient maximum likelihood estimation for the developed regression models.
  • Simulation studies confirm the satisfactory performance of the quantile estimation method.

Conclusions:

  • The novel class of distributions and associated regression models offer a robust framework for analyzing complex multivariate positive data.
  • The methodology is effective for quantile estimation and parameter estimation in challenging datasets.
  • The approach demonstrates practical utility through an application to newborn data analysis.