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Local influence in comparative calibration models under elliptical t-distributions.

Manuel Galea1, Heleno Bolfarine, Filidor Vilca

  • 1Departamento de Estadística, Universidad de Valparaíso, Casilla 5030, Valparaíso, Chile. manuel.galea@uv.cl

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Summary

This study applies local influence methods to structural comparative calibration under elliptical distributions. It evaluates model and data perturbations for robust analysis using real-world data.

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Area of Science:

  • Statistics
  • Statistical Modeling

Background:

  • Local influence analysis assesses model sensitivity to small perturbations.
  • Structural comparative calibration is used for comparing calibration models.
  • Elliptical distributions offer a flexible framework for multivariate data.

Purpose of the Study:

  • To investigate the application of local influence diagnostics in structural comparative calibration.
  • To evaluate the impact of various perturbation schemes on calibration models.
  • To demonstrate the utility of these methods with a real data set.

Main Methods:

  • Applying local influence (Cook, 1986) diagnostics.
  • Utilizing structural comparative calibration (Bolfarine and Galea, 1995).
  • Assuming multivariate elliptical distributions for measurement errors.
  • Investigating different perturbation schemes.
  • Employing the elliptical t-distribution for a case study.

Main Results:

  • The study identifies how local influence can detect influential perturbations in structural comparative calibration.
  • Perturbation schemes effectively reveal model or data set sensitivities.
  • The elliptical t-distribution provides a practical case for applying these methods.

Conclusions:

  • Local influence is a valuable tool for assessing the robustness of structural comparative calibration models.
  • The methodology is applicable to real-world data exhibiting elliptical distributions.
  • Understanding perturbation effects enhances the reliability of calibration results.