Trace of the Variance-Covariance Matrix in Natural Exponential Families |
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| Authors: | Taher Ben Arab Afif Masmoudi Mourad Zribi |
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| Institution: | 1. Laboratory of Statistics and Probability, Sfax University, Sfax, Tunisia;2. Laboratoire d’Informatique Signal et Image de la C?te d’Opale, Calais, FranceTaher.ben_arab@yahoo.fr;4. Laboratoire d’Informatique Signal et Image de la C?te d’Opale, Calais, France |
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| Abstract: | In this article, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. Under some conditions, we prove that this trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belongs to some NEFs. Therefore, we introduce the estimator of this trace variance function. We give the asymptotic properties of this estimator. Finally, we illustrate our results using a simulation study. |
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| Keywords: | Asymptotic properties Estimator Mean parameter Natural exponential family Trace Variance function |
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