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Distance-Based Estimation Methods for Models for Discrete and Mixed-Scale Data.

Elisavet M Sofikitou1, Ray Liu2, Huipei Wang1

  • 1Department of Biostatistics, University at Buffalo, Buffalo, NY 14214, USA.

Entropy (Basel, Switzerland)
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PubMed
Summary
This summary is machine-generated.

Pearson residuals help detect statistical model errors by comparing data-driven estimates with null hypothesis models. New formulations address mixed-scale data, improving model misspecification identification and estimator robustness.

Keywords:
contingency tablesdisparitymixed-scale datapearson residualsresidual adjustment functionrobustnessstatistical distances

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Data Analysis

Background:

  • Pearson residuals are crucial for identifying statistical model misspecification.
  • Comparing estimated models with null hypothesis models is key to residual analysis.
  • Existing methods may not fully address data measured on mixed scales.

Purpose of the Study:

  • To present novel formulations of Pearson residual systems adaptable to various data measurement scales.
  • To investigate the properties of these new residual systems, particularly for mixed-scale data.
  • To study the asymptotic properties and robustness of minimum disparity estimators for mixed-scale data.

Main Methods:

  • Development of different Pearson residual system formulations.
  • Analysis of residual properties considering categorical and interval scale data.
  • Investigation of asymptotic properties and robustness of minimum disparity estimators.
  • Performance evaluation through simulation studies.

Main Results:

  • The proposed Pearson residual formulations effectively handle different measurement scales.
  • The methods demonstrate robustness and desirable asymptotic properties for mixed-scale data.
  • Simulation results exemplify the practical performance of the developed techniques.

Conclusions:

  • The enhanced Pearson residual systems provide a valuable tool for model misspecification detection, especially with mixed-scale data.
  • Minimum disparity estimators show promise for robust statistical inference in mixed-scale data scenarios.
  • Further research can build upon these methods for advanced statistical modeling.