Orthogonal regression method for observations from a mixture
Authors:
R. E. Maĭboroda, G. V. Navara and O. V. Sugakova
Translated by:
S. V. Kvasko
Journal:
Theor. Probability and Math. Statist. 99 (2019), 169-188
MSC (2010):
Primary 62G05, 62G20; Secondary 62J05
DOI:
https://doi.org/10.1090/tpms/1088
Published electronically:
February 27, 2020
MathSciNet review:
3908664
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Additional Information
Abstract: A generalization of the orthogonal regression method is considered for estimating parameters of the simple linear regression model with errors in variables for observations from a mixture with varying concentrations. The consistency and asymptotic normality is proved for the estimators studied in the paper. The dispersion matrix is established.
References
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- R. Maĭboroda and O. Sugakova, Estimation and Classification by Using Observations from a Mixture, “Kyiv University”, Kyiv, 2008. (in Ukrainian)
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References
- C.-L. Cheng and J. Van Ness, Statistical Regression with Measurement Error, Kendall’s Library of Statistics 6, Arnold, London, 1999. MR 1719513
- R. Maĭboroda and O. Sugakova, Estimation and Classification by Using Observations from a Mixture, “Kyiv University”, Kyiv, 2008. (in Ukrainian)
- S. Masiuk, A. Kukush, S. Shklyar, M. Chepurny, and I. Likhtarov (eds.), Radiation Risk Estimation: Based on Measurement Error Models, 2nd ed., de Gruyter series in Mathematics and Life Sciences, vol. 5, de Gruyter, 2017. MR 3726857
- T. Benaglia, D. Chauveau, D. Hunter, and D. Young, mixtools: An R Package for Analyzing Finite Mixture Models, J. Stat. Software 32 (2009), no. 6, 1–29.
- S. Faria and G. Soromenhob, Fitting mixtures of linear regressions, J. Stat. Computation and Simulation 80 (2010), no. 2, 201–225. MR 2757044
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- R. Branham, Total Least Squares in Astronomy, Total Least Squares and Errors-in-Variables Modeling, Springer, Dordrecht, 2002, pp. 375–384. MR 1952962
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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
G. V. Navara
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:
mrswade111017@gmail.com
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:
Model of a mixture,
orthogonal regression,
method of generalized estimating equations
Received by editor(s):
March 4, 2018
Published electronically:
February 27, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
