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Unified extension of variance bounds for integrated Pearson family

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Abstract

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function \(g(X)\) of an absolutely continuous random variable \(X\), in terms of the derivatives of \(g\) up to some order. The new bounds are better than the existing ones.

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Acknowledgments

From this position I would like to thank Professor N. Papadatos for his helpful observations and comments. I would also like to thank an anonymous Associate Editor who carefully read the revised manuscript and kindly brought to my attention a typing error in the proof of Lemma 1.

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Authors and Affiliations

  1. Department of Mathematics, Section of Statistics and O.R., University of Athens, Panepistemiopolis, 157 84 , Athens, Greece

    Giorgos Afendras

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  1. Giorgos Afendras
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Correspondence to Giorgos Afendras.

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Afendras, G. Unified extension of variance bounds for integrated Pearson family. Ann Inst Stat Math 65, 687–702 (2013). https://doi.org/10.1007/s10463-012-0388-3

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  • DOI: https://doi.org/10.1007/s10463-012-0388-3

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