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Estimating Gaussian Copulas with Missing Data with and without Expert Knowledge.

Maximilian Kertel1,2, Markus Pauly2,3

  • 1BMW Group, Battery Cell Competence Centre, 80788 Munich, Germany.

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|December 23, 2022
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Summary
This summary is machine-generated.

This study applies the Expectation Maximization algorithm to Gaussian copula models with missing data, improving distribution accuracy. Incorporating expert knowledge further enhances results for robust statistical analysis.

Keywords:
expectation maximizationexpert knowledgemissing at randomsemiparametric estimation

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Gaussian copula models are widely used for multivariate data analysis.
  • Handling missing data in statistical models presents significant challenges.
  • A priori assumptions on marginal distributions can limit model flexibility.

Purpose of the Study:

  • To apply the Expectation Maximization (EM) algorithm for Gaussian copula models with missing data.
  • To develop semiparametric approaches to avoid assumptions on marginal distributions.
  • To integrate expert knowledge into the model for improved accuracy.

Main Methods:

  • Rigorous application of the Expectation Maximization algorithm.
  • Semiparametric modeling to address marginal distribution assumptions.
  • Incorporation of domain expertise for marginals and dependency structure.

Main Results:

  • The EM algorithm accurately determines marginal distributions and dependence structure.
  • Semiparametric modeling successfully circumvents a priori assumptions.
  • Integration of expert knowledge yields superior distribution learning compared to existing methods.
  • Simulation studies confirm the enhanced accuracy of the proposed approach.

Conclusions:

  • The proposed EM-based Gaussian copula model effectively handles missing data.
  • Semiparametric and expert knowledge integration enhance model robustness and accuracy.
  • This methodology offers a powerful tool for complex data analysis in statistics and machine learning.