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Czasopismo

2011 | 9 | 2 | 281-293

Tytuł artykułu

Generalized covariance inequalities

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
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.

Wydawca

Czasopismo

Rocznik

Tom

9

Numer

2

Strony

281-293

Opis fizyczny

Daty

wydano
2011-04-01
online
2011-02-18

Twórcy

  • Marie Curie-Skłodowska University
  • Marie Curie-Skłodowska University

Bibliografia

  • [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
  • [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
  • [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
  • [4] Chung K.L., A Course in Probability Theory, 3rd ed., Academic Press, San Diego, 2001
  • [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] 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
  • [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
  • [8] Lehmann E.L., Some concepts of dependence, Ann. Math. Statist., 1966, 37(5), 1137–1153 http://dx.doi.org/10.1214/aoms/1177699260
  • [9] Matuła P., On some inequalities for positively and negatively dependent random variables with applications, Publ. Math. Debrecen, 2003, 63(4), 511–522
  • [10] Matuła P., A note on some inequalities for certain classes of positively dependent random variables, Probab. Math. Statist., 2004, 24(1), 17–26
  • [11] Nelsen R.B., An Introduction to Copulas, 2nd ed., Springer Ser. Statist., Springer, New York, 2006
  • [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] 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
  • [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] 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
  • [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

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_s11533-011-0006-2
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