Proceedings of International Conference on Applied Innovation in IT  ·  2026/03/31  ·  Vol. 14  ·  Issue 1  ·  pp. 115–121
Multivariate Partial Linear Modeling for Groundwater Quality Anaiysis
Huda Yahay Ahmed and Emad Hazim Aboudi
📄 Download PDF DOI: 10.25673/123543
Abstract
This research aims to estimate the multivariate partial linear model using two methods: Profile Least Squares and Profile Likelihood, with the goal of identifying the factors affecting the decline in groundwater quality in two geographical locations within Baghdad city (Abu Ghraib and Mahmudiya). The main problem lies in the presence of several response variables that are correlated with each other within the same model, which complicates the process of accurate estimation of the parameters. Additionally, there are correlations between the response variables and the explanatory variables, further challenging the estimation process. The model includes both linear and nonlinear variables, adding to the complexity of the analysis. Total dissolved solids and ion ratios were used as response variables, while the independent variables included sodium, chloride, and sulfate. The geographical location was incorporated as a nonparametric component in the analysis. The two methods were compared based on the Mean Squared Error (MSE) criterion to determine the preferred method for model estimation. Real data were used to verify the effectiveness of the methods in practical applications, and the results indicated the superiority of the Profile Least Squares method in providing more accurate and reliable estimates of the model.
Keywords
Profile Least Squares Profile Likelihood Multivariate Partial Linear Kernel Smoother.
References
  1. W. Häardie and M. Müller, “Multivariate and Semiparametric Kernel Regression,” pp. 357-391, 2000, [Online]. Available: https://doi.org/10.1002/9781118150658.ch12.
  2. L. D. Brown, M. Levine, and L. Wang, “A semiparametric multivariate partially linear model: A difference approach,” J. Stat. Plan. Inference, vol. 178, pp. 99-111, 2016, [Online]. Available: https://doi.org/10.1016/j.jspi.2016.06.005.
  3. M. Levine, “Robust functional estimation in the multivariate partial linear model,” Ann. Inst. Stat. Math., vol. 71, no. 4, pp. 743-770, 2019, [Online]. Available: https://doi.org/10.1007/s10463-018-0661-1.
  4. J. Zhang, B. Lin, and Y. Zhou, “Kernel density estimation for partial linear multivariate responses models,” J. Multivar. Anal., vol. 185, p. 104768, 2021, [Online]. Available: https://doi.org/10.1016/j.jmva.2021.104768.
  5. S. Meng and Z. Huang, “Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data,” Mathematics, vol. 12, no. 17, 2024, [Online]. Available: https://doi.org/10.3390/math12172778.
  6. Q. Wu, X. Tong, and X. Zhao, “Deep partially linear cox model for current status data,” Biometrics, vol. 80, no. 2, pp. 1-12, 2024, [Online]. Available: https://doi.org/10.1093/biomtc/ujae024.
  7. M. Przystalski, “Estimation of the covariance matrix in multivariate partially linear models,” J. Multivar. Anal., vol. 123, pp. 380-385, 2014, [Online]. Available: https://doi.org/10.1016/j.jmva.2013.09.005.
  8. B. Pateiro-López and W. González-Manteiga, “Multivariate partially linear models,” Stat. Probab. Lett., vol. 76, no. 14, pp. 1543-1549, 2006, [Online]. Available: https://doi.org/10.1016/j.spl.2006.03.016.
  9. Z. Li, L. Su, and D. Zhang, “Profile least squares estimation of a partially linear time trend model with weakly dependent data,” Econ. Lett., vol. 125, no. 3, pp. 404-407, 2014, [Online]. Available: https://doi.org/10.1016/j.econlet.2014.10.030.
  10. Y. Zhang and L. Zhu, “Semiparametric estimation of multivariate partially linear models,” J. Stat. Comput. Simul., vol. 87, no. 11, pp. 2115-2127, 2017, [Online]. Available: https://doi.org/10.1080/00949655.2017.1318135.
  11. S. A. Murphy and A. W. van der Vaart, “On Profile Likelihood: Rejoinder,” J. Am. Stat. Assoc., vol. 95, no. 450, p. 482, 2000, [Online]. Available: https://doi.org/10.2307/2669392.
  12. J. Fan and T. Huang, “Profile likelihood inferences on semiparametric varying-coefficient partially linear models,” Bernoulli, vol. 11, no. 6, pp. 1031-1057, 2005, [Online]. Available: https://doi.org/10.3150/bj/1137421639.
  13. N. H. Timm, Applied Multivariate Analysis, Springer Texts in Statistics. New York, NY: Springer, 2002. doi: 10.1007/b98963.

Proceedings of the International Conference on Applied Innovations in IT by Anhalt University of Applied Sciences is licensed under CC BY-SA 4.0  ·  This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

ICAIIT 2026
International Conference on Applied Innovation in IT
Navigation
Publisher
ISSN2199-8876
Publisher Edition Hochschule Anhalt
Location Anhalt University of Applied Sciences
Email leiterin.hsb@hs-anhalt.de
Phone +49 (0) 3496 67 5611
Address Building 01, Room 425
Bernburger Str. 55
D-06366 Köthen, Germany
Open Access License
CC BY-SA 4.0

All works are licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0), unless otherwise noted.

Published by ICAIIT in cooperation with Anhalt University of Applied Sciences.

© 2026 ICAIIT — International Conference on Applied Innovations in IT. Anhalt University of Applied Sciences, Köthen, Germany.
Visitors: site traffic counter