Parameter estimation by minimizing a probability generating function-based power divergence |
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Authors: | S. Y. Tay S. H. Ong |
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Affiliation: | 1. Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia;2. Department of Actuarial Science and Applied Statistics, UCSI University, Kuala Lumpur, Malaysia |
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Abstract: | AbstractGenerating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases. |
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Keywords: | Density power divergence Hellinger distance Jeffreys’ divergence M-estimation Probability generating function |
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