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Trace of the Variance-Covariance Matrix in Natural Exponential Families

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Listed:
  • Taher Ben Arab
  • Afif Masmoudi
  • Mourad Zribi

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.

Suggested Citation

  • Taher Ben Arab & Afif Masmoudi & Mourad Zribi, 2015. "Trace of the Variance-Covariance Matrix in Natural Exponential Families," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(6), pages 1241-1254, March.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:6:p:1241-1254
    DOI: 10.1080/03610926.2012.762400
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