A weighted maximum likelihood method (WMLM) of robust estimation of experimental data with outliers is proposed in this work. The method allows effective robust asymptotically unbiased estimates to be obtained under conditions of aprioristic uncertainty. Based on the WMLM, adaptive robust algorithms have been synthesized for solving semiparametric and semi-nonparametric problems of heterogeneous data processing. It is shown that for heterogeneous data samples, these estimates converge to the maximum likelihood estimates for each distribution from the Tukey supermodel not only in the presence of major, but also minor asymmetric and symmetric outliers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V.A. Fedorov, Opt. Atmos. Okeana, 16, No. 02, 151–155 (2003).
R. Muthukrishnan and G. Poonkuzhali, Am.-Eur. J. Sci. Res., 12, No. 3, 161–171 (2017).
V. A. Simakhin, O. S. Tcherepanov, and L. G. Shamanaeva, Russ. Phys. J., 58, No. 12, 1868–1874 (2016).
P. J. Huber, Robust Statistics [Russian translation], Mir, Moscow (1984).
F. R. Hampel, E. M. Ronchetti, P. J. Rousseuw, and W. A. Stahel, Robust Statistics: The Approach Based on Influence Functions [Russian translation], Mir, Moscow (1989).
V. A. Simakhin, Robust Nonparametric Estimates, Lambert Academic Publishing, Saarbrücken (2011).
A. M. Shurygin, Applied Statistics. Robustness. Estimation. Prediction, Finansy Statistika, Moscow (2000).
Ya. Z. Tsypkin, Fundamentals of Information Theory of Identification [in Russian], Nauka, Moscow (1995).
V. P. Shulenin, Robust Methods of Mathematical Statistics [in Russian], Publishing House of Tomsk Scientific and Technology Literature, Tomsk (2016).
R. V. Hogg, Comm. Statist., 11, 2531–2542 (1982).
M. Markatou, A. Basu, and B. G. Lindsay, J. Am. Statist. Assoc., 57, 740–750 (1998).
C. Agostinelli, Stat. Probab. Lett., 76, 1930–1934 (2006).
B. G. Lindsay, Ann. Statist., 22, 1018–1114 (1994).
C. Park, A. Basu, and B. G. Lindsay, Comput. Statist. Data Anal., 39, 21–33 (2002).
L. A. Jaeckel, Ann. Math. Statist., 42, 1020–1034 (1971).
C. J. Stone, Ann. Statist., 3, No. 2, 267–284 (1975).
R. Beran, Ann. Statist., 6, 292–313 (1978).
A. A. Borovkov, Mathematical Statistics [in Russian], Nauka, Novosibirsk (1997).
V. A. Simakhin, L. G. Shamanaeva, and A. E. Avdyushina, Russ. Phys. J., 63, No. 9, 1510–1518 (2021).
L. Devroye and L. Györfi, Nonparametric Density Estimation: The L1 View [Russian translation], Mir, Moscow (1988).
A. V. Dobrovidov and G. M. Koshkin, Nonparametric Estimation of Signals [in Russian], Nauka, Moscow (1997).
Yu. N. Tyurin, in: Lecture Notes in Statistics. Vol. 26 [in Russian], Nauka, Moscow (1974), pp. 7–24.
Yu. G. Dmitriev, in: Mathematical Statistics and Its Applications, Issue 11 [in Russian], Publishing House of Tomsk State University (1987), pp. 39–46.
Yu. G. Dmitriev and G. M. Koshkin, Avtom. Telemekh., No. 10, 47–59 (1987).
Yu. G. Dmitriev and G. M. Koshkin, Statist. Pap., 59, No. 4, 1559–1575 (2018).
S. Bradley, Atmospheric Acoustic Major Sensing, Boca Raton; London; New York, CRC Press. Taylor & Fransis Group (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 149–158, February, 2021.
Rights and permissions
About this article
Cite this article
Simakhin, V.A., Shamanaeva, L.G. & Avdyushina, A.E. Robust Semiparametric and Semi-Nonparametric Estimates of Inhomogeneous Experimental Data. Russ Phys J 64, 355–366 (2021). https://doi.org/10.1007/s11182-021-02336-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11182-021-02336-z