Generalized covariance inequalities

• Autorzy: Przemysław Matuła , Maciej Ziemba
• 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.

Słowa kluczowe

EN

Covariance; Copula; Positive and negative dependence; Probabilistic inequalities; Kernel estimation

Kategorie tematyczne

• 60F25: L p -limit theorems
• 62G07: Density estimation
• 62H20: Measures of association (correlation, canonical correlation, etc.)
• 60E15: Inequalities; stochastic orderings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 281-293

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Przemysław Matuła

• Marie Curie-Skłodowska University,

autor

Maciej Ziemba

• 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

Identyfikatory

DOI

10.2478/s11533-011-0006-2