Examining of Air Pollutant Concentrations in Baghdad: A Semiparametric Approach Using Robust Estimation Techniques
DOI:
https://doi.org/10.62933/rn535k81Keywords:
Additive Partial linear Regression Model. , Generalized least-squares. , Restrictions. , Multicollinearity., Ridge Estimators. , LTS- Estimators. , Local Polynomial Smoother., Air Quality Index (AQI).Abstract
The article aims to provide a precise understanding of the multiple factors affecting air quality in Baghdad. This was achieved through rigorous modeling of air quality data within the frame of the restricted partially linear additive regression model, focusing on enhancing the efficiency and robustness of ridge estimates. addresses challenges related to multicollinearity and outliers present in the response variable observations. By employing an integrative methodology that combines robust ridge estimates with non-random restriction imposed on the parametric component. and using the Generalized least squares (GLS) method, which addresses issues of heteroscedasticity and improves parametric estimates. Meanwhile, the Least Trimmed Squares (LTS) method effectively handles outliers by trimming the data to enhance the accuracy of estimates and reduce the impact of outliers. This, in turn, facilitated a smoother transition to the nonparametric component, which was smoothed using the Local Polynomial Estimator method, suitability of the graphical representations of the estimated functions for the two nonparametric variables.
Additionally, a comprehensive evaluation of the performance and efficiency of the semiparametric model was conducted using comparison criteria such as the Mean Absolute Deviation (MAD) and the Coefficient of Determination (R²). The air quality data collected during the summer of 2023 was meticulously modeled to achieve this. The integration of robust ridge estimates, employing the LTS method, with the imposition of non-random restriction on the parameters demonstrated significant effectiveness in estimating the homogeneity functions Include the model’s components.
Furthermore, the applied analysis revealed intriguing non-linear relationships between certain explanatory variables and the dependent variable. specially, PM10, representing particulate matter with a 10-micrometer diameter, along with carbon dioxide (CO2), had the most pronounced effect on the Air Quality Index (AQI). This knowledge underscores the importance of implementing preventive measures aimed at safeguarding public health.
References
1. Abonazel, M. R, and Gad, A. A. E. (2020). Robust partial residuals estimation in semiparametric partially linear models. Communications in Statistics - Simulation and Computation, 49(5), 1223-1236.
2. Ali, O. A., & Kazem, K. J. (2023). Weighted Least Squares Estimation of the Effect of Wastewater Pollution of Tigris River / Wasit Governorate. Journal of Engineering and Applied Sciences, 24(109). https://doi.org/10.33095/jeas.v24i109.1573.
3. Arashi, M, and Roozbeh, M. (2013). Feasible ridge estimator in partially linear models. Journal of Multivariate Analysis, 114, 35-44.
4. Arzideh, K, and Emami, H. (2022). Robust ridge estimator in censored semiparametric linear models. Communications in Statistics - Theory and Methods. https://doi.org/10.1080/03610926.2021.2023573.
5. Dai, D, and Wang, D. (2023). A generalized Liu-type estimator for logistic partial linear regression models with multicollinearity. AIMS Mathematics, 5, 11851–11874. https://doi.org/10.3934/math.2023600.
6. El-Gohary, M, Abonazel, R., Helmy, M. M., and Azazy, R. A. (2019). New robust-ridge estimators for partially linear models. International Journal of Applied Mathematical Research, 8(2), 46-52. https://doi.org/10.14419/ijamr.v8i2.29932.
7. Emami, H. (2016). Local influence in ridge semiparametric models. Journal of Statistical Computation and Simulation. https://doi.org/10.1080/00949655.2016.1152273.
8. Gai, Y., Zhang, J, Li, G, and Luo, X. (2015). Statistical inference on partial linear additive models with distortion measurement errors. Statistical Methodology, 20-38. https://doi.org/10.1016/J.STAMET.2015.05.004
9. Gibbons, D. G. (1981). A simulation study of some ridge estimators. Journal of the American Statistical Association, 76(373), 131–139. https://doi.org/10.2307/2287058.
10. Härdle, W, Linton, O. (1994). Applied nonparametric methods. In R. F. Engle and D. McFadden (Eds.), Handbook of Econometrics (pp. 2295-2339).
11. Härdle, W, Mammen, E. (1993). Comparing nonparametric versus parametric regression fits. The Annals of Statistics, 21(4), 1926-1947.
12. Härdle, W, Müller, M, Sperlich, S, and Werwatz, A. (2004). Nonparametric and semiparametric models.
13. Härdle, W., Liang, H, and Gao, J. (2000). Partially linear models. Springer Science and Business Media.
14. Hoerl, A. E, and Kennard, R. W. (1970). Ridge regression: Biased estimation for non-orthogonal problems. Technometrics, 12(1), 69-82.
15. Hoerl, A. E, and Kennard, R. W. (2000). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 42(1), 80–86. https://doi.org/10.2307/1271436.
16. Hoerl, A. E, Kennard, R. W, and Baldwin, K. F. (1975). Ridge regression: Some simulation. Communications in Statistics - Simulation and Computation, 4, 105-123.
17. Jiang, Y, Tian, G. L, and Fei, Y. (2019). A robust and efficient estimation method for partially nonlinear models via a new MM algorithm. Statistical Papers, 60, 2063–2085. https://doi.org/10.1007/s00362-017-0909-5.
18. Jiang, Y. (2017). S-estimator in partially linear regression models. Journal of Applied Statistics, 6, 968-977. https://doi.org/10.1080/02664763.2016.1189523.
19. Kaciranlar, S, Sakallioglu, S, Ozkale, M. R., and Guler, H. (2011). More on the restricted ridge regression estimation. Journal of Statistical Computation and Simulation, 81, 1433–1448.
20. Keller, G, and Warrack, B. (2000). Statistics for Managing and Economics (5th ed.).
21. Kingsley, C. A, and Fidelis, I. U. (2022). Combining principal component and robust ridge estimators in linear regression models with multicollinearity and outliers. Concurrency and Computation: Practice and Experience. https://doi.org/10.1002/cpe.6803.
22. Kuran, Ö, and Yalaz, S. (2023). Kernel mixed and kernel stochastic restricted ridge predictions in partially linear mixed measurement error models: An application to COVID-19. Journal of Applied Statistics, 1-25.
23. Li, L, and Yin, X. (2008). Sliced inverse regression with regularizations. Biometrics, 64(1), 124-131.
24. Liu, R, and Yang, L. (2010). Spline-backfitted kernel smoothing of additive coefficient models. Econometric Theory, 26(1), 29-59.
25. Liu, R. Y, and Yang, L. (2009). Efficient estimation of a semiparametric partially linear varying-coefficient model. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71, 447-466.
26. Opsomer, J. D, and Kauermann, G. (2004). Generalized cross-validation for bandwidth selection of backfitting estimates in generalized additive models. Journal of Computational and Graphical Statistics, 13(1), 66-89.
27. Opsomer, J. D, and Ruppert, D. (1998). A fully automated bandwidth selection method for fitting additive models. Journal of the American Statistical Association, 93(443), 605-619.
28. Opsomer, J. D, and Ruppert, D. (1999). A root-inconsistent backfitting estimator for semiparametric additive modeling. Journal of Computational and Graphical Statistics, 8(4), 715-732.
29. Rousseeuw, P. J, and Leroy, A. M. (2005). Robust regression and outlier detection. John Wiley and Sons.
30. Rousseeuw, P. J, and Van Zomeren, B. C. (1990). Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association, 85, 633–639.
31. Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79(388), 871-880.
32. Swamy, P. A. V. B, and others. (1978). Two methods of evaluating Hoerl and Kennard’s ridge regression. Communications in Statistics - Theory and Methods, 7(11), 1133-1155.
33. Tukey, J. W. (1960). A survey of sampling from contaminated distributions. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling (pp. 448-485).
34. World Health Organization - Air quality guidelines (2023).
35. Wu, J. and Asar, Y. (2017). A weighted stochastic restricted ridge estimator in partially linear models. Communications in Statistics - Theory and Methods. https://doi.org/10.1080/03610926.2016.1206936.
36. Yang, J. and Yang, H. (2017). Robust modal estimation and variable selection for single-index varying-coefficient models. Communications in Statistics - Simulation and Computation, 4, 2976-2997. https://doi.org/10.1080/03610918.2015.1069346.
37. Zhang, W, and Huang, J. (2014). Variable selection in partially linear additive models for longitudinal/clustered data. Journal of the Royal Statistical Society.
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