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Deterministic, quenched, and annealed parameter estimation for heterogeneous network models.

Marzio Di Vece1,2, Diego Garlaschelli1,3,4, Tiziano Squartini1,2,4,5

  • 1IMT School for Advanced Studies, Piazza San Francesco 19, 55100 Lucca, Italy.

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The annealed estimation method is superior to the deterministic approach for continuous, conditional network models. This finding integrates econometric and statistical physics models for economic system analysis.

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Area of Science:

  • Network analysis
  • Statistical modeling
  • Economic systems

Background:

  • Two main statistical approaches exist for economic system analysis: econometrics and statistical physics.
  • Recent work integrated these by minimizing Kullback-Leibler divergence, creating integrated and conditional models.
  • Distinct parameter estimation methods are used in each approach.

Purpose of the Study:

  • To compare different parameter estimation recipes for continuous, conditional network models.
  • To determine the most effective estimation method by comparing econometric and statistical physics approaches.

Main Methods:

  • The study compares deterministic, quenched, and annealed estimation methods.
  • Focus is on continuous, conditional network models within an integrated framework.
  • Analysis involves comparing parameter estimation strategies based on averaging and maximization orders.

Main Results:

  • The annealed estimation recipe is identified as the best alternative to the deterministic one.
  • This finding is specific to continuous, conditional network models.
  • The study highlights the impact of averaging and maximization order on parameter estimation.

Conclusions:

  • The annealed estimation method offers a more robust approach for analyzing economic networks compared to deterministic methods.
  • This research provides valuable insights for selecting appropriate statistical models and estimation techniques in econometrics and network science.
  • The findings contribute to the ongoing integration of statistical physics and econometric methodologies.