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Simulation Studies of a Hölder Perturbation in a New Estimator for Proportion Considering Extra-Binomial Variability
Estudios de simulación de una perturbación Hölder en un nuevo estimador de proporción considerando la variabilidad extra-binomial
DOI:
https://doi.org/10.15446/rce.v38n1.48803Keywords:
Binomial Distribution, Monte Carlo simulation, Robust Estimator, Robustness (en)Distribución binomial, Estimador robusto, Simulación Monte Carlo, Robustez. (es)
This present work aims to propose an estimator in order to estimate the probability of success of a binomial model that incorporates the extrabinomial variation generated by zero-inflated samples. The construction of this estimator was carried out with a theoretical basis given by the Holder function and its performance was evaluated through Monte Carlo simulation considering different sample sizes, parametric values (π), and excess of zero proportions (γ). It was concluded that for the situations in (γ = 0.20) and (γ = 0.50) that the proposed estimator presents promising results based on the specified margin of error.
El presente trabajo tiene como objetivo proponer un estimador para estimar la probabilidad de éxito de un modelo binomial que incorpora la variación extra-binomial generada por muestras cero-inflados. La construcción de este estimador se llevó a cabo con una base teórica dada por la función Holder y su desempeño fue evaluado a través de la simulación de Monte Carlo considerando diferentes tamaños de muestra, valores paramétricos (), y el exceso de proporciones cero ( ). Se concluyó que para las situaciones en ( = 0,20) y ( = 0,50) que el estimador propuesto presenta resultados prometedores basados en el margen de error especificado.
References
Achcar, J. A. & Junqueira, J. G. (2002), ‘Extra-binomial variability: A Bayesian approach’, Journal of Statistical Research 36, 1–14.
Basu, A., Shiyoa, H. & Park, C. (2011), Statistical Inference: The Minimum Distance Approach, Chapman and Hall.
Begehr, H. G. W. (1994), Complex Analytic Methods for Partial Differential Equations: An Introductory Text, World Scientific, Singapore.
Hinde, S. & Demetrio, G. G. B. (1978), ‘Overdispersion models and estimation’, Computational Statistics & Data Analysis 34, 69–76.
Huber, P. (1964), ‘Robust estimation of a location paramenter.’, Annals of Mathematical Statistics 35, 73–101.
Kupper, L. L. & Haseman, J. K. (1998), ‘The use of a correlated binomial model for the analysis of certain toxicological experiments’, Biometrics 27, 151–170.
Lindsay, B. G. (1994), ‘Efficiency versus robustness: The case for mínimum Hellinger distance and related methods’, The Annals of Statistics 22, 1081–1114.
Park, C., Basu, A. & Lindsay, B. (2002), ‘The residual adjustment function and weighted likelihood: a graphical interpretation of robustness of mínimum disparity estimators’, Computational Statistics and Data Analysis 39, 21–33.
R Development Core Team (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
Ruckstuhl, A. F. & Welsh, A. H. (2001), ‘Robust fitting of the binomial model’, The Annals of Statistics 29, 1117–1136.
Silva, A. M. & Cirillo, M. A. (2010), ‘Estudo por simulação Monte Carlo de um estimador robusto utilizado na inferência de um modelo binomial contaminado’, Acta Scientiarum. Technology 32, 303–307.
Simpson, D. G. (1987), ‘Minimum Hellinger distance estimation for the analysis of count data’, Journal of the American Statistical Association 82, 802–807.
Simpson, D. G., Carrol, R. J. & Ruppert, D. (1987), ‘M-estimation for discrete data: Asymptoptic distribution theory and implications’, The Annals of Statistics 15(2), 657–669.
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