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Prediction in Riemannian metrics derived from divergence functions

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  • Henryk Gzyl

Abstract

Divergence functions are interesting and widely used discrepancy measures. Even though they are not true distances we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables they lead to a notion of best predictor that coincides with usual best predictor in Euclidean distance. From a divergence function we can derive a Riemannian metric which leads to a true distance between random variables, and the best predictors in this metric do not coincide with their Euclidean counterparts. It is the purpose of this paper to explicitly determine the best predictors in the derived metric, compare it to the estimators in divergence, and to obtain the sample estimators of the best predictors. Along the way we obtain results that relate approximations in divergence to approximations in the metric derived from it.

Suggested Citation

  • Henryk Gzyl, 2022. "Prediction in Riemannian metrics derived from divergence functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(2), pages 552-568, January.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:2:p:552-568
    DOI: 10.1080/03610926.2020.1752384
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