Generalized covariance inequalities

Przemysław Matuła; Maciej Ziemba

Open Mathematics (2011)

  • Volume: 9, Issue: 2, page 281-293
  • ISSN: 2391-5455

Abstract

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We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.

How to cite

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Przemysław Matuła, and Maciej Ziemba. "Generalized covariance inequalities." Open Mathematics 9.2 (2011): 281-293. <http://eudml.org/doc/269449>.

@article{PrzemysławMatuła2011,
abstract = {We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.},
author = {Przemysław Matuła, Maciej Ziemba},
journal = {Open Mathematics},
keywords = {Covariance; Copula; Positive and negative dependence; Probabilistic inequalities; Kernel estimation; covariance; copula; positive and negative dependence; probabilistic inequalities; kernel estimation},
language = {eng},
number = {2},
pages = {281-293},
title = {Generalized covariance inequalities},
url = {http://eudml.org/doc/269449},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Przemysław Matuła
AU - Maciej Ziemba
TI - Generalized covariance inequalities
JO - Open Mathematics
PY - 2011
VL - 9
IS - 2
SP - 281
EP - 293
AB - We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.
LA - eng
KW - Covariance; Copula; Positive and negative dependence; Probabilistic inequalities; Kernel estimation; covariance; copula; positive and negative dependence; probabilistic inequalities; kernel estimation
UR - http://eudml.org/doc/269449
ER -

References

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  1. [1] Bagai I., Prakasa Rao B.L.S., Estimation of the survival function for stationary associated processes, Statist. Probab. Lett., 1991, 12(5), 385–391 http://dx.doi.org/10.1016/0167-7152(91)90027-O Zbl0749.62057
  2. [2] Bulinski A., Shashkin A., Limit Theorems for Associated Random Fields and Related Systems, Adv. Ser. Stat. Sci. Appl. Probab., 10, World Scientific, Hackensack, 2007 Zbl1154.60037
  3. [3] Cai Z., Roussas G.G., Smooth estimate of quantiles under association, Statist. Probab. Lett., 1997, 36(3), 275–287 http://dx.doi.org/10.1016/S0167-7152(97)00074-6 Zbl0946.62039
  4. [4] Chung K.L., A Course in Probability Theory, 3rd ed., Academic Press, San Diego, 2001 
  5. [5] Etemadi N., Stability of sums of weighted nonnegative random variables, J. Multivariate Anal., 1983, 13, 361–365 http://dx.doi.org/10.1016/0047-259X(83)90032-5 
  6. [6] Karlin S., Rinott Y., Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions, J. Multivariate Anal., 1980, 10(4), 467–498 http://dx.doi.org/10.1016/0047-259X(80)90065-2 Zbl0469.60006
  7. [7] Kotz S., Balakrishnan N., Johnson N.L., Continuous Multivariate Distributions, 2nd ed., Wiley Ser. Probab. Statist. Appl. Probab. Statist., Wiley, New York, 2000 http://dx.doi.org/10.1002/0471722065 Zbl0946.62001
  8. [8] Lehmann E.L., Some concepts of dependence, Ann. Math. Statist., 1966, 37(5), 1137–1153 http://dx.doi.org/10.1214/aoms/1177699260 Zbl0146.40601
  9. [9] Matuła P., On some inequalities for positively and negatively dependent random variables with applications, Publ. Math. Debrecen, 2003, 63(4), 511–522 Zbl1048.60016
  10. [10] Matuła P., A note on some inequalities for certain classes of positively dependent random variables, Probab. Math. Statist., 2004, 24(1), 17–26 Zbl1061.60013
  11. [11] Nelsen R.B., An Introduction to Copulas, 2nd ed., Springer Ser. Statist., Springer, New York, 2006 Zbl1152.62030
  12. [12] Newman C.M., Asymptotic independence and limit theorems for positively and negatively dependent random variables, In: Inequalities in Statistics and Probability, Lincoln, 1982, Inst Math. Statist., Hayward, 1984, 127–140 http://dx.doi.org/10.1214/lnms/1215465639 
  13. [13] Rodríguez-Lallena J.A., Úbeda-Flores M., A new class of bivariate copulas, Statist. Probab. Lett., 2004, 66(3), 315–325 http://dx.doi.org/10.1016/j.spl.2003.09.010 Zbl1102.62054
  14. [14] Roussas G.G., Kernel estimates under association: strong uniform consistency, Statist. Probab. Lett., 1991, 12(5), 393–403 http://dx.doi.org/10.1016/0167-7152(91)90028-P 
  15. [15] Schweizer B., Wolff E.F., On nonparametric measures of dependence for random variables, Ann. Statist., 1981, 9(4), 879–885 http://dx.doi.org/10.1214/aos/1176345528 Zbl0468.62012
  16. [16] Yu H., A Glivenko-Cantelli lemma and weak convergence for empirical processes of associated sequences, Probab. Theory Related Fields, 1993, 95(3), 357–370 http://dx.doi.org/10.1007/BF01192169 

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