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On upper bounds for the variance of functions of random variables

Author

Listed:
  • Cacoullos, T.
  • Papathanasiou, V.

Abstract

The upper bounds for the variance of a function g of a random variable X obtained in Cacoullos (1982) (for short CP) are improved in the case [mu] = E(X) [not equal to] 0. A main feature of these bounds is that they involve the second moment of the derivative or the difference of g. A multivariate extension for functions of independent random variables is also given.

Suggested Citation

  • Cacoullos, T. & Papathanasiou, V., 1985. "On upper bounds for the variance of functions of random variables," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 175-184, July.
    • Handle: RePEc:eee:stapro:v:3:y:1985:i:4:p:175-184
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    Citations

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    Cited by:

    1. Salinelli, Ernesto, 2009. "Nonlinear principal components, II: Characterization of normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 652-660, April.
    2. V. Papathanasiou, 1995. "A characterization of the Pearson system of distributions and the associated orthogonal polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(1), pages 171-176, January.
    3. Goodarzi, F. & Amini, M. & Mohtashami Borzadaran, G.R., 2016. "On upper bounds for the variance of functions of the inactivity time," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 62-71.
    4. Giorgos Afendras & Vassilis Papathanasiou, 2014. "A note on a variance bound for the multinomial and the negative multinomial distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 179-183, April.
    5. Mohtashami Borzadaran, G. R. & Shanbhag, D. N., 1998. "Further results based on Chernoff-type inequalities," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 109-117, August.
    6. Papadatos, N. & Papathanasiou, V., 1996. "A generalization of variance bounds," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 191-194, June.
    7. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    8. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    9. Giorgos Afendras, 2013. "Unified extension of variance bounds for integrated Pearson family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 687-702, August.

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