Comparison the Robust Estimators Nonparametric of Nonparametric Regressions
Article Sidebar
Main Article Content
Abstract
In order to get rid of or reduce the abnormal values of some phenomena that may be the reason for not obtaining the desired results. This makes us to get conclusions far from reality for the phenomenon we are studying. That the traditional nonparametric estimators are very sensitive to anomalous values, which prompted us to use the fortified estimators because they are not much affected by the anomalous values, as well as the nonparametric regression because it does not depend on the previous determinants or assumptions, but it depends directly and fundamentally on the data.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] Dilmaç, H., & Şişman, Y. New approaches for outlier detection: The least trimmed squares adjustment. International Journal of Engineering and Geosciences, 8(1), 26-31.
[2] M. Wand and B. Ripley, “KernSmooth: Functions for kernel smoothing for Wand & Jones (1995),” R Packag. version, vol. 2, p. 19–22, 2006.
[3] CM Hurvich, JS Simonoff, and C. Tsai, “Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion,” JR Stat. Soc. Ser. B (Statistical Methodol., vol. 60, no. 2, pp. 271–293, 1998.
[4] Blanchett. J and Wadsworth. J. (2012). 5. "Applied Statistics", Institute of Mathematics, Analysis, and Applications EPF Lausanne An MSc Course for Applied Mathematicians, working paper.
[5] Racine, JS (2008). Nonparametric econometrics: A primer. Foundations and Trends® in Econometrics, 3(1), 1-88.
[6] Midi, H., Rana, MS, & Imon, AHMR (2009). The performance of robust weighted least squares in the presence of outliers and heteroscedastic errors. WSEAS Transactions on Mathematics, 8(7), 351-361.
[7] Hardle W. (1994), "Applied Nonparametric Regression", Gambridg MA: Cambirg University Press.
[8] Aydin D. (2007), "A Comparison of the Nonparametric Regression Models using Smoothing Spline and Kernel Regression", World Academy of Science, Engineering and Technology.
[9] Demir, S., & Toktamiş, Ö. (2010). On the adaptive Nadaraya-Watson kernel regression estimators. Hacettepe Journal of Mathematics and Statistics, 39(3), 429-437.
[10] Turlach, BA (1993, January). Bandwidth selection in kernel density estimation: A review. In CORE and Institut de Statistique. 11. Wand, MP, & Jones, MC (1994). Kernel smoothing. Chapman and Hall/CRC.
[11] KOUASSI, BC, Hili, O., & KATCHEKPELE, E. (2021). Nadaraya-Watson estimation of a nonparametric autoregressive model. Malaya Journal of Matematik, 9(4), 251-258.
[12] Cheng C.-B.& Lee ES, (1999), “Nonparametric fuzzy regressionk-NN and kernel smoothing techniques” Computers and Mathematics with Applications, 38, 239–251
[13] Wanas, MS, & AL-Sharoat, MH (2020). Studying some approaches to estimate the smoothing parameter for the nonparametric regression model. Periodicals of Engineering and Natural Sciences, 8(2), 673-683.
[14] Michael G. Schimek (2000), "Smoothing and Regression (Approaches, Computation, and Application)", University of Graz and University of Vienna, Karl-Franzens, Austria
[15] Gibran Abdel-Amir, Korkis Shahid, Muhammad Salem (2018), Estimating the parameters of multiple linear regression using robust methods (a comparative study), Al-Qadisiyah Journal of Computer Science and Mathematics, Volume (8), Issue (1), p. 12-21.
[16] Rosenblatt, M. (1956). Remarks on Some Nonparametric Estimates of a Density Function. The Annals of Mathematical Statistics, 27(3), 832-837.
[17] R. Marona, R. Martin, VJ Yohai. 2006. Robust Statistics Theory and Methods. John Wiley & Sons Ltd., England.
[18] Härdle, W. (1984). Robust regression function estimation. Journal of Multivariate Analysis, 14(2), 169-180. [
[19] Huber, PJ, (1964). "Robust Estimation of location parameter." Ann .math .stat.35-73-101.
[20] Fox, J., & Weisberg, S. (2012). Robust regression. An R and S-Plus companion to applied regression, 91.
[21] Deribati, MM, Younso, A., & Al-shakh, D. Converges in of nearest neighbor regression function estimate for strong mixing processes 1.
[22] Chen C., (2002), “Robust regression and outlier detection with the Robustreg procedure” In Proceedings of the Twenty Seventh Annual SAS Users Group International Conference; SAS Institute: Cary, NC.
[23] Y. Susanti, H. Pratiwi, and T. Liana, Application of Mestimation to Predict Paddy Production in Indonesia, presented at IndoMS International Conference on Mathematics and Its Applications (IICMA), Yogyakarta, 2009.
[24] Yuliana and Y. Susanti, Estimasi M dan sifat-sifatnya pada Regresi Linear Robust, Jurnal Math-Info, 1, No. 11 (2008), 8-16.
[25] Y. Susanti and H. Pratiwi, Robust Regression Model for Predicting the Soybean Production in Indonesia, Canadian Journal on Scientific and Industrial Research, 2, No. 9 (2011), 318-328.
[26] Rasheed, BA, Adnan, R., Saffari, SE, & dano Pati, K. (2014). Robust weighted least squares estimation of regression parameter in the presence of outliers and heteroscedastic errors. Jurnal Teknologi, 71(1).
[27] HAWGLEN, DC, MOSTELLER, F & TUKEY, JW (1983) Understanding Robust and Exploratory Data Analysis. Wiley, New York.
[28] France, Jiri"Robust regression: Robust Estimation of Regression Coefficient in Linear Regression Model when orthogonality condition.
[29] Andrews, DF, Bickel, PJ, Hampel, FR, Huper, PJ, Rogers, WH, and Tukey, JW (1972). “Robust estimates of location: Survey and advances.” Princeton University Press , Princeton ,NJ
[30] M. Dr.. Ibtisam Karim Abdullah, & Hussein Karim Nashour. (2019). Estimates of least squares and least squares trimmed for linear regression with skewed normal errors. Journal of Administration and Economics, 1(121), 377-388
[31] Zuo, Y. (2022). Asymptotic normality of the least sum of squares of trimmed residuals estimator. arXiv preprint arXiv:2204.00700.
[32] Zuo, Y. (2022). Least sum of squares of trimmed residuals regression. arXiv preprint arXiv: 2202.10329.
[33] Zuo, Y. (2022). New algorithms for computing the least trimmed squares estimator. arXiv preprint arXiv: 2203.10387.
[34] Denis H. and Yan L. (2005), "Cross-Validation in Nonparametric Regression with Outliers", The Annals of Statistics, Vol. 33, No. 5, pp.2291-2310.
[35] Luo, S., & Zhang, CY (2016). Nonparametric $$ M $$ M-type regression estimation under missing response data. Statistical Papers, 57(3), 641-664.