Abstract
For the data of sampling from a mixture of several components with varying concentrations, we construct nonparametric estimates for the distributions of components and determine the rank correlation coefficient. We prove the consistency of the rank coefficient and the efficiency of the estimates of distributions.
References
H. Teicher, “Identifiability of mixtures,” Ann. Math. Statist., 32, No. 1, 244–248 (1961).
S. A. Aivazyan, et al., Applied Statistics. Classification and Reduction of Dimensionality [in Russian], Finansy i Statistika, Moscow (1989).
R. E. Maiboroda, “Projective estimates for mixtures with varying concentrations,” Teor. Ver. Mat. Statist., 44, 87–92 (1991).
R. E. Maiboroda, “Estimators for parameters of time-dependent mixture concentrations,” Dokl. Akad. Nauk Ukr., 4, 34–37 (1993).
C. J. Stone, “Consistent nonparametric regression,” Ann. Statist., 5, 595–645 (1977).
P. Billingsley, Convergence of Probability Measures, Wiley, New York 1968.
R. M. Dudly, “Central limit theorems for empirical measures,” Arm. Probab., 6, No. 6, 899–929 (1978).
I. A. Ibragimov and R. Z. Khas’minskii, Asymptotic Theory of Estimation [in Russian], Nauka, Moscow 1979.
Y. Valdi, “Empirical distributions in selection bias models,” Ann, Statist., 13, No. 1, 198–203 (1985).
A. Owen, “Empirical likelihood ratio confidence intervals for single functional,” Biometrika, 75, 237–249 (1988).
R. D. Gill and A. W. Van der Vaart, “Non- and semi-parametric maximum likelihood estimators and the von Mises method II,” Scand. J. Statist., 20, 271–288 (1993).
R. E. Maiboroda, “On the estimation of parameters of varying mixtures,” Teor. Ver. Mat. Statist., 44, 87–92 (1991).
A. A. Borovkov, Mathematical Statistics [in Russian], Nauka, Moscow 1984.
Rights and permissions
About this article
Cite this article
Maiboroda, R.E. Estimates for distributions of components of mixtures with varying concentrations. Ukr Math J 48, 618–622 (1996). https://doi.org/10.1007/BF02390622
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02390622