New robust-ridge estimators for partially linear model

  • Authors

    • Mervat M. Elgohary Faculty of Commerce (Girls Branch), Al-Azhar University
    • Mohamed R. Abonazel Faculty of Graduate Studies for Statistical Research, Cairo University
    • Nahed M. Helmy Faculty of Commerce (Girls Branch), Al-Azhar University
    • Abeer R. Azazy Faculty of Commerce (Girls Branch), Al-Azhar University
    2019-11-17
    https://doi.org/10.14419/ijamr.v8i2.29932
  • Least Trimmed Squares, Monte Carlo Simulation, Spline Smoothing, Semi-Parametric Regression, Ridge Regression, Robust Regression

  • This paper considers the partially linear model when the explanatory variables are highly correlated as well as the dataset contains outliers. We propose new robust biased estimators for this model under these conditions. The proposed estimators combine least trimmed squares and ridge estimations, based on the spline partial residuals technique. The performance of the proposed estimators and the Speckman-spline estimator has been examined by a Monte Carlo simulation study. The results indicated that the proposed estimators are more efficient and reliable than the Speckman-spline estimator.

     

     

  • References

    1. [1] Abonazel, M. R. (2018a). Different estimation methods of partially linear regression models. Working paper. Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.

      [2] Abonazel, M. R. (2018b). A practical guide for creating Monte Carlo simulation studies using R. International Journal of Mathematics and Computational Science, 4(1), 18-33.

      [3] Abonazel, M. R. (2019). New ridge estimators of SUR model when the errors are serially correlated. International Journal of Mathematical Archive, 10(7):53-62.

      [4] Abonazel, M. R. & Farghali, R. A. (2018). Liu-type multinomial logistic estimator. Sankhya B: The Indian Journal of Statistics. https://doi.org/10.1007/s13571-018-0171-4.

      [5] Abonazel, M. R., & Gad, A. A. (2018). Robust partial residuals estimation in semiparametric partially linear model. Communications in Statistics-Simulation and Computation, 1-14. https://doi.org/10.1080/03610918.2018.1494279.

      [6] Abonazel, M. R., Helmy, N. & Azazy, A. (2019). The performance of Speckman estimation for partially linear model using kernel and spline smoothing approaches. International Journal of Mathematical Archive, 10(6):10-18.

      [7] Ahn, H., & Powell, J. L. (1993). Semiparametric estimation of censored selection models with a nonparametric selection mechanism. Journal of Econometrics, 58(1-2), 3-29. https://doi.org/10.1016/0304-4076(93)90111-H.

      [8] Amini, M., & Roozbeh, M. (2016). Least trimmed squares ridge estimation in partially linear regression models. Journal of Statistical Computation and Simulation, 86(14):2766-2780.†https://doi.org/10.1080/00949655.2015.1128433.

      [9] Arslan, O., & Billor, N. (1996). Robust ridge regression estimation based on the GM-estimators. Journal of Mathematical and Computational Science, 9(1), 1-9.

      [10] Aydın, D. (2014). Estimations of the partially linear models with smoothing spline based on different selection methods: a comparative study. Pakistan Journal of Statistics, 30(1), 35-56.

      [11] Chen, H., & Shiau, J. J. H. (1991). A two-stage spline smoothing method for partially linear models. Journal of Statistical Planning and Inference, 27(2), 187-201. https://doi.org/10.1016/0378-3758(91)90015-7.

      [12] El-Sayed, S. M., Abonazel, M. R., & Seliem, M. M. (2019), B-Spline Speckman Estimator of Partially Linear Model. Working paper. Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.

      [13] Engle, R. F., Granger, C. W., Rice, J., & Weiss, A. (1986). Semiparametric estimates of the relation between weather and electricity sales. Journal of the American statistical Association, 81(394), 310-320. https://doi.org/10.1080/01621459.1986.10478274.

      [14] Fadili, J. M., & Bullmore, E. (2005). Penalized partially linear models using sparse representations with an application to fMRI time series. IEEE Transactions on signal processing, 53(9), 3436-3448. https://doi.org/10.1109/TSP.2005.853207.

      [15] Hamilton, S. A., & Truong, Y. K. (1997). Local linear estimation in partly linear models. Journal of Multivariate Analysis, 60(1), 1-19. https://doi.org/10.1006/jmva.1996.1642.

      [16] Härdle, W., Liang, H., & Gao, J. (2000). Partially linear models. Springer Science & Business Media. https://doi.org/10.1007/978-3-642-57700-0.

      [17] Härdle, W. K., Müller, M., Sperlich, S., & Werwatz, A. (2004). Nonparametric and semiparametric models. Springer Science & Business Media. https://doi.org/10.1007/978-3-642-17146-8.

      [18] Kaçıranlar, S., & Dawoud, I. (2018). On the performance of the Poisson and the negative binomial ridge predictors. Communications in Statistics-Simulation and Computation, 47(6):1751-1770.†https://doi.org/10.1080/03610918.2017.1324978.

      [19] Kan, B., Alpu, Ö, & Yazıcı, B. (2013) robust ridge and robust Liu estimator for regression based on the LTS estimator. Journal of Applied Statistics, 40(3):644-655. https://doi.org/10.1080/02664763.2012.750285.

      [20] Kibria, B. G. (2003). Performance of some new ridge regression estimators. Communications in Statistics-Simulation and Computation, 32(2):419-435. https://doi.org/10.1081/SAC-120017499.

      [21] Månsson, K., & Shukur, G. (2011). On ridge parameters in logistic regression. Communications in Statistics-Simulation and Computation, 40:3366–3381. https://doi.org/10.1080/03610926.2010.500111.

      [22] Roozbeh, M. (2016). Robust ridge estimator in restricted semiparametric regression models. Journal of Multivariate Analysis, 147:127-144.†https://doi.org/10.1016/j.jmva.2016.01.005.

      [23] Speckman, P. (1988). Kernel smoothing in partial linear models. Journal of the Royal Statistical Society: Series B (Methodological), 50(3), 413-436. https://doi.org/10.1111/j.2517-6161.1988.tb01738.x,

      [24] Yatchew, A. (1997). An elementary estimator of the partial linear model. Economics Letters, 57(2), 135–143. https://doi.org/10.1016/S0165-1765(97)00218-8.

      [25] Yatchew, A. (2000). Scale economies in electricity distribution: a semiparametric analysis. Journal of Applied Econometrics, 15(2), 187–210. https://doi.org/10.1002/(SICI)1099-1255(200003/04)15:2<187::AID-JAE548>3.0.CO;2-B.

      [26] Yatchew, A. (2003). Semiparametric regression for the applied econometrician. Cambridge University Press. https://doi.org/10.1017/CBO9780511615887.

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  • How to Cite

    M. Elgohary, M., R. Abonazel, M., M. Helmy, N., & R. Azazy, A. (2019). New robust-ridge estimators for partially linear model. International Journal of Applied Mathematical Research, 8(2), 46-52. https://doi.org/10.14419/ijamr.v8i2.29932