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

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.