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Entropy 2018, 20(5), 329; https://doi.org/10.3390/e20050329

Minimum Penalized ϕ-Divergence Estimation under Model Misspecification

1
Departamento de Estadística e Investigación Operativa, Universidad de Jaén, 23071, Jaén, Spain
2
Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, 41012, Sevilla, Spain
3
Departamento de Ingeniería Cartográfica, Geodésica y Fotogrametría, Universidad de Jaén, 23071, Jaén, Spain
*
Author to whom correspondence should be addressed.
Received: 8 March 2018 / Revised: 22 April 2018 / Accepted: 27 April 2018 / Published: 30 April 2018
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Abstract

This paper focuses on the consequences of assuming a wrong model for multinomial data when using minimum penalized ϕ -divergence, also known as minimum penalized disparity estimators, to estimate the model parameters. These estimators are shown to converge to a well-defined limit. An application of the results obtained shows that a parametric bootstrap consistently estimates the null distribution of a certain class of test statistics for model misspecification detection. An illustrative application to the accuracy assessment of the thematic quality in a global land cover map is included. View Full-Text
Keywords: minimum penalized ϕ-divergence estimator; consistency; asymptotic normality; goodness-of-fit; bootstrap distribution estimator; thematic quality assessment minimum penalized ϕ-divergence estimator; consistency; asymptotic normality; goodness-of-fit; bootstrap distribution estimator; thematic quality assessment
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Alba-Fernández, M.V.; Jiménez-Gamero, M.D.; Ariza-López, F.J. Minimum Penalized ϕ-Divergence Estimation under Model Misspecification. Entropy 2018, 20, 329.

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