Geodesic
Probability of sign coincidence centered with respect to sample mean random variables
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2018), pp. 23-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Probability of sign coincidence of centered random variables is one possible measure of connection. In [4] it was shown that the measure does not depend from generating function in the class of elliptically contoured distributions. This result was obtained for known shift parameter. In the present paper it is proved that for any sample size the probability of sign coincidence centered with respect to the sample mean random variables does not depend on generating function too. Moreover it is proved that the probability of sign coincidence centered with respect to the sample mean random variables is equal to the probability of sign coincidence centered with respect to the shift parameter random variables.
Keywords: matrix elliptically contoured distribution, probability of sign coincidence, invariance with respect to generating function, invariance with respect to shift parameter. 
@article{VTPMK_2018_4_a1,
     author = {P. A. Koldanov},
     title = {Probability of sign coincidence centered with respect to sample mean random variables},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {23--30},
     year = {2018},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a1/}
}
TY  - JOUR
AU  - P. A. Koldanov
TI  - Probability of sign coincidence centered with respect to sample mean random variables
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2018
SP  - 23
EP  - 30
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a1/
LA  - ru
ID  - VTPMK_2018_4_a1
ER  - 
%0 Journal Article
%A P. A. Koldanov
%T Probability of sign coincidence centered with respect to sample mean random variables
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2018
%P 23-30
%N 4
%U http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a1/
%G ru
%F VTPMK_2018_4_a1
P. A. Koldanov. Probability of sign coincidence centered with respect to sample mean random variables. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2018), pp. 23-30. http://geodesic.mathdoc.fr/item/VTPMK_2018_4_a1/

[1] Anderson T. W., An Introduction to Multivariate Statistical Analysis, 3rd edition, John Wiley and Sons, New York, 2003, 721 pp. | MR

[2] Kruskal W. H., “Ordinal measures of association”, Journal of the American Statistical Association, 53:284 (1958), 814–861 | DOI | MR | Zbl

[3] Gupta A. K., Varga T., Bodnar T., Elliptically Contoured Models in Statistics and Portfolio Theory, Springer-Verlag, New York, 2013, 321 pp. | DOI | MR | Zbl

[4] Kalyagin V. A., Koldanov A. P., Koldanov P. A., “Robust identification in random variable networks”, Journal of Statistical Planning and Inference, 181 (2017), 30–40 | DOI | MR | Zbl