Correlation analysis of mixtures. II. (English. Ukrainian original) Zbl 0927.62060

Maiboroda, R. E.

Theory Probab. Math. Stat. 55, 129-133 (1997); translation from Teor. Jmovirn. Mat. Stat. 55, 125-129 (1996).

[For part I see the preceding review, Zbl 0927.62059]
The author considers the data \(\xi_j=(\xi_j(1),\xi_j(2))\), which are independent 2-dimensional random vectors of observations of mixtures with \(M\) components, \[ P\{\xi_j \in A\}=\sum_{k=1}^Mw_j(k)H_k(A), \] where \(H_k\) is the distribution function of the \(k\) th component (unknown), and \(w_j(k)\) is the probability to obtain an object from the \(k\) th population at the \(j\) th observation. Coefficients which generalize the Spearman \(\rho\) and Kendall \(\tau\) are considered. Consistency and asymptotic normality of these coefficients are examined. It is shown that the jackknife method gives a.s. consistent estimates of the limit variation of the Spearman \(\rho\) and Kendall \(\tau\) coefficients. The bootstrap method is applied to investigate the problem.

Reviewer: M.P.Moklyachuk (Kyïv)

MSC:

62H20	Measures of association (correlation, canonical correlation, etc.)
62G09	Nonparametric statistical resampling methods
60F17	Functional limit theorems; invariance principles

Keywords:

mixtures; correlation analysis; correlation coefficient; asymptotic normality; consistency

Citations:

Zbl 0927.62059