Cross-validation for local-linear regression by observations from mixture

Authors

DOI:

https://doi.org/10.17721/1812-5409.2023/1.5

Keywords:

Mixture with varying concentrations, Nonparametric regression, Cross-validation technique, Local-linear regression

Abstract

We consider a generalization of local-linear regression for estimation of compnents' regression functions by observations from mixture with varying concentrations. A cross-validation technique is developed for the bahdwidth selection. Performance of the obtained estimator is compared with the modified Nadaraya-Watson estimator performance by simulations.

Pages of the article in the issue: 37 - 43

Language of the article: Ukrainian

References

MAIBORODA R., SUGAKOVA O. (2008) Otsiniuvannia ta klasyfikatsiia za sposterezhenniamy iz sumishi. Kyiv: Kyivskyi universytet, 213 p.

A. PIDNEBESNA, I. FAJNEROV'A, J. HOR'Av{C}EK, J. HLINKA. (2023)

Mixture Components Inference for Sparse Regression: Introduction and Application for Estimation of Neuronal Signal from fMRI BOLD. In Applied Mathematical Modelling, Vol. 116, p. 735-748.

DYCHKO H., MAIBORODA R. (2020) A generalized Nadaraya–Watson estimator for observations obtained from a mixture. In Theory of Probability and Mathematical Statistics, Vol. 100, p. 61-76, DOI: 10.1090/tpms/1098.

NADARAYA E. (1964) On Estimating Regression. In Theory of Probability and its Applications, Vol. 9, No. 1, p. 141-142.

WATSON G. (1964) Smooth regression analysis. In Sankhya: The Indian Journal of Statistics, Series A, Vol. 26, No. 4, p. 359-372.

FAN J. (1993) Local Linear Regression Smoothers and their minimax efficiencies. In The Annals of Statistics, Vol. 21, No. 1, p. 196-216.

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Published

2023-07-13

How to Cite

Horbunov, D., & Maiboroda, R. (2023). Cross-validation for local-linear regression by observations from mixture. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 37–43. https://doi.org/10.17721/1812-5409.2023/1.5

Issue

No. 1 (2023)

Section

Algebra, Geometry and Probability Theory

License

Copyright (c) 2023 Daniel Horbunov, Rostyslav Maiboroda

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