A correlation coefficient for angular variables. (English) Zbl 0738.62069
Statistical theory and data analysis II, Proc. 2nd Pac. Area Stat. Conf., Tokyo/Jap. 1986, 349-364 (1988).
[For the entire collection see Zbl 0732.00018.]
A circular correlation coefficient which has all the desirable properties of a correlation coefficient is defined. The paper amplifies and provides some further details on a definition that was given by J. S. Rao and Y. R. Sarma [Proc. ISI 44th session, Vol. 2, 571-574 (1983)]. A sample analogue of the measure is introduced and its asymptotic distribution is obtained. The third section deals with some parametric models and illustrates how the definition given in section 2 works for these models. In these special cases, estimates of the proposed measure and their asymptotic distributions are derived. These estimates are then used to test hypotheses concerning angular correlations. Finally a nonparametric correlation coefficient is introduced in section 4.
A circular correlation coefficient which has all the desirable properties of a correlation coefficient is defined. The paper amplifies and provides some further details on a definition that was given by J. S. Rao and Y. R. Sarma [Proc. ISI 44th session, Vol. 2, 571-574 (1983)]. A sample analogue of the measure is introduced and its asymptotic distribution is obtained. The third section deals with some parametric models and illustrates how the definition given in section 2 works for these models. In these special cases, estimates of the proposed measure and their asymptotic distributions are derived. These estimates are then used to test hypotheses concerning angular correlations. Finally a nonparametric correlation coefficient is introduced in section 4.
MSC:
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 62E20 | Asymptotic distribution theory in statistics |
| 62F03 | Parametric hypothesis testing |
