Tests of hypotheses on quantiles of distributions of components in a mixture
Authors:
R. E. Maĭboroda and O. V. Sugakova
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 101 (2020), 179-191
MSC (2020):
Primary 62G08; Secondary 62G20
DOI:
https://doi.org/10.1090/tpms/1120
Published electronically:
January 5, 2021
Full-text PDF
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Additional Information
Abstract: The problem of testing statistical hypotheses concerning quantiles of different distributions of components in a mixture with varying concentrations is considered. Homogeneity of medians or that of interquartile ranges in different components are two possible examples of such kind of hypotheses. Estimators for quantiles in a model of mixtures with varying concentrations are presented. Sufficient conditions for the asymptotic normality of these estimators are obtained. Asymptotic confidence ellipsoids and tests for linear hypotheses based on these estimators are constructed. The quality of procedures proposed in this paper is checked for samples of finite sizes with the help of simulation results.
References
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References
- F. Autin and C. Pouet, Minimax rates over Besov spaces in ill-conditioned mixture-models with varying mixing-weights, J. Stat. Plann. Inference 146 (2014), 20–30. MR 3132476
- P. J. Bickel and M. J. Wichura, Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statist. 42 (1971), no. 5, 1656–1670. MR 383482
- A. Doronin and 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. MR 3316487
- M. Hollander, D. A. Wolfe, and E. Chicken, Nonparametric Statistical Methods, 3rd edition, John Wiley & Sons, Hoboken, 2014. MR 3221959
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- J. W. Tukey, Exploratory Data Analysis, Addison Wesley, Reading, MA, 1977.
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Additional Information
R. E. Maĭboroda
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
mre@univ.kiev.ua
O. V. Sugakova
Affiliation:
Department of Mathematics and Theoretical Radiophysics, Faculty for Radiophysics, Electronics, and Computer Systems, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
sugak@univ.kiev.ua
Keywords:
A model of a mixture with varying concentrations,
quantiles,
asymptotic normality,
linear hypothesis
Received by editor(s):
August 30, 2019
Published electronically:
January 5, 2021
Article copyright:
© Copyright 2020
American Mathematical Society
