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Homogeneity of multinomial populations when data are classified into a large number of groups.

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Minimum Penalized ϕ-Divergence Estimation under Model Misspecification.

M Virtudes Alba-Fernández1, M Dolores Jiménez-Gamero2, F Javier Ariza-López3

  • 1Departamento de Estadística e Investigación Operativa, Universidad de Jaén, 23071, Jaén, Spain.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

Incorrect model assumptions for multinomial data using minimum penalized disparity estimators lead to predictable parameter estimation limits. Parametric bootstrap methods can consistently estimate null distributions for detecting model misspecification.

Keywords:
asymptotic normalitybootstrap distribution estimatorconsistencygoodness-of-fitminimum penalized ϕ-divergence estimatorthematic quality assessment

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Area of Science:

  • Statistics
  • Statistical Modeling
  • Data Analysis

Background:

  • Minimum penalized ϕ-divergence estimators are used for parameter estimation in multinomial data.
  • Model misspecification can significantly impact the reliability of statistical inference.

Purpose of the Study:

  • To investigate the consequences of using incorrect models with minimum penalized disparity estimators.
  • To establish the convergence properties of these estimators under model misspecification.
  • To demonstrate the utility of parametric bootstrap for detecting model misspecification.

Main Methods:

  • Theoretical analysis of minimum penalized ϕ-divergence estimators under model misspecification.
  • Convergence analysis of the estimators.
  • Application of parametric bootstrap for estimating null distributions of test statistics.

Main Results:

  • The estimators converge to a well-defined limit even when the model is misspecified.
  • Parametric bootstrap provides a consistent method for estimating the null distribution of test statistics used for model misspecification detection.

Conclusions:

  • Minimum penalized disparity estimators exhibit robustness to certain types of model misspecification.
  • Parametric bootstrap is a reliable tool for assessing model adequacy in multinomial data analysis.
  • The findings have practical implications for evaluating thematic accuracy in land cover mapping.