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Prediction and estimation of random variables with infinite mean or variance

Author

Listed:
  • Victor de la Peña
  • Henryk Gzyl
  • Silvia Mayoral
  • Haolin Zou
  • Demissie Alemayehu

Abstract

In this article, we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and finite variance. The proposed predictor is a generalized arithmetic mean which is similar to the notion of certainty price in utility theory. Typically, the transformation consists of a parametric family of bijections, in which case the parameter might be chosen to minimize the prediction error in the transformed coordinates. The statistical properties of the estimator of the proposed predictor are studied, and confidence intervals are provided. The performance of the procedure is illustrated using simulated and real data.

Suggested Citation

  • Victor de la Peña & Henryk Gzyl & Silvia Mayoral & Haolin Zou & Demissie Alemayehu, 2025. "Prediction and estimation of random variables with infinite mean or variance," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(1), pages 115-129, January.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:1:p:115-129
    DOI: 10.1080/03610926.2024.2303976
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