Theory of Probability and Mathematical Statistics
Tests on quantiles of mixture components' distributions
R. E. Maiboroda, O. V. Sugakova
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Abstract: The hypotheses testing problem is considered for hypotheses on quantiles of different components of a mixture with varying concentrations.
Keywords:
Bibliography: f medians or interquartile ranges can be considered as the examples. Estimates for the quantiles are presented, their
asymptotic normality is demonstrated. Asymptotic confidence ellipsoids and tests for linear hypotheses are constructed. Simulation results are presented.
Bibliography: 1. F. Autin, C. Pouet, Minimax rates over Besov spaces in ill-conditioned mixture-models with varying mixing-weights, Journal of Statistical Planning and Inference, 146 (2014), 20-30.
2. P. J. Bickel, M. J. Wichura, Convergence criteria for multipapameter stochastic processes and some applications, Ann. Math. Statist., 42 (1971), no. 5, 1656-1670.
3. A. Doronin, R. Maiboroda, Testing hypotheses on moments by observations from a mixture with varying concentrations, Modern Stochastics: Theory and Applications, 1 (2014), no. 2, 195-209.
4. M. Hollander, D. A. Wolfe, E. Chicken, Nonparametric Statistical Methods, John Wiley & Sons, Hoboken, 2014.
5. R. E. Maiboroda, Statistical analysis of mixtures, Kyiv University Publishers, Kyiv, 2003. (In Ukrainian)
6. R. E. Maiboroda, O. V. Sugakova, Esitmation and classi cation by observations from a mixture, Kyiv University Publishers, Kyiv, 2008. (In Ukrainian)
7. R. E. Maiboroda, A test for the homogeneity of mixtures with varying concentrations, Ukrainian Mathematical Journal, 52 (2000), no. 8, 1256-1263.
8. G. J. McLachlan, D. Peel, Finite mixture models, Wiley-Interscience, 2000.
9. G. J. McLachlan, K.-A. Do, C. Ambroise, Analyzing Microarray Gene Expression Data, Wiley-Interscience, 2004.
10. G. J. Myatt, W. P. Johnson, Making Sense of Data I: A Practical Guide to Exploratory Data Analysis and Data Mining, Willey, Hoboken, 2014.
11. A. Yu. Ryzhov, A test of the hypothesis about the homogeneity of components of a mixture with varying concentrations by using censored data, Theory Probab. Math. Statist., 72 (2006), 145-155.
12. J. Shao, Mathematical statistics, Springer-Verlag, New York, 1998.
13. J. W. Tukey, Exploratory Data Analysis, Addison Wesley, Reading MA, 1977.
