Volume 4, Issue 4, December 2019, Page: 53-59
B-spline Speckman Estimator of Partially Linear Model
Sayed Meshaal El-sayed, Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
Mohamed Reda Abonazel, Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
Mohamed Metwally Seliem, Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
Received: Aug. 25, 2019;       Accepted: Dec. 31, 2019;       Published: Feb. 3, 2020
DOI: 10.11648/j.ijssam.20190404.12      View  471      Downloads  101
The partially linear model (PLM) is one of semiparametric regression models; since it has both parametric (more than one) and nonparametric (only one) components in the same model, so this model is more flexible than the linear regression models containing only parametric components. In the literature, there are several estimators are proposed for this model; where the main difference between these estimators is the estimation method used to estimate the nonparametric component, since the parametric component is estimated by least squares method mostly. The Speckman estimator is one of the commonly used for estimating the parameters of the PLM, this estimator based on kernel smoothing approach to estimate nonparametric component in the model. According to the papers in nonparametric regression, in general, the spline smoothing approach is more efficient than kernel smoothing approach. Therefore, we suggested, in this paper, using the basis spline (B-spline) smoothing approach to estimate nonparametric component in the model instead of the kernel smoothing approach. To study the performance of the new estimator and compare it with other estimators, we conducted a Monte Carlo simulation study. The results of our simulation study confirmed that the proposed estimator was the best, because it has the lowest mean squared error.
Kernel Smoothing, Monte Carlo Simulation, Penalized B-spline Estimation, Semiparametric Regression, Spline Smoothing
To cite this article
Sayed Meshaal El-sayed, Mohamed Reda Abonazel, Mohamed Metwally Seliem, B-spline Speckman Estimator of Partially Linear Model, International Journal of Systems Science and Applied Mathematics. Vol. 4, No. 4, 2019, pp. 53-59. doi: 10.11648/j.ijssam.20190404.12
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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.
Heckman, N. E. (1986). Spline smoothing in a partly linear model. Journal of the Royal Statistical Society: Series B (Methodological), 48 (2), 244-248.
Rice, J. (1986). Convergence rates for partially splined models. Statistics & probability letters, 4 (4), 203-208.
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.
Abonazel, M. R., & Gad, A. A. E. (2018). Robust partial residuals estimation in semiparametric partially linear model. Communications in Statistics-Simulation and Computation, 1-14.
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.
Robinson, P. M. (1988), Root-N-consistent semiparametric regression. Econometrica, 56 (4), 931–54.
Speckman, P. (1988). Kernel smoothing in partial linear models. Journal of the Royal Statistical Society: Series B (Methodological), 50 (3), 413-436.
Hamilton, S. A., & Truong, Y. K. (1997). Local linear estimation in partly linear models. Journal of Multivariate Analysis, 60 (1), 1-19.
Carroll, R. J., Fan, J., Gijbels, I., & Wand, M. P. (1997). Generalized partially linear single-index models. Journal of the American Statistical Association, 92 (438), 477-489.
Yatchew, A. (1997). An elementary estimator of the partial linear model. Economics Letters, 57 (2), 135–143.
Yatchew, A. (2000). Scale economies in electricity distribution: a semiparametric analysis. Journal of Applied Econometrics, 15 (2), 187–210.
Yatchew, A. (2003). Semiparametric regression for the applied econometrician. Cambridge University Press.
Wang, L., Brown, L. D., & Cai, T. T. (2011). A difference based approach to the semiparametric partial linear model. Electronic Journal of Statistics, 5, 619-641.
Henderson, D. J., & Parmeter, C. F. (2015). Single-step estimation of a partially linear model. Working Papers, University of Miami, Department of Economics. Available at: https://www.bus.miami.edu/_assets/files/repec/WP2015-01.pdf
Elgohary, M. M., Abonazel, M. R., Helmy, N. M., & Azazy, A. R. (2019). New robust-ridge estimators for partially linear model. International Journal of Applied Mathematical Research, 8 (2): 46-52.
Green, P. J., & Silverman, B. W. (1994). Nonparametric regression and generalized linear models: a roughness penalty approach. Chapman and Hall/CRC.
Ruppert, D., Wand, M. P., & Carroll, R. J. (2003). Semiparametric regression (No. 12). Cambridge university press.
Wasserman, L. (2006). All of nonparametric statistics. Springer Science & Business Media.
De Boor, C. (1978). A practical guide to splines. (Vol. 27, p. 325). New York: springer-verlag.
Eilers, P. H., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11 (2), 89-102.
Eilers, P. H., & Marx, B. D. (2010). Splines, knots, and penalties. Wiley Interdisciplinary Reviews: Computational Statistics, 2 (6), 637-653.
Eilers, P. H., Marx, B. D., & Durbán, M. (2015). Twenty years of P-splines. Statistics and Operations Research Transactions, 39 (2), 0149-186.
Marx, B. D., & Eilers, P. H. (1999). Generalized linear regression on sampled signals and curves: a P-spline approach. Technometrics, 41 (1), 1-13.
Abonazel, M. R. (2018). A practical guide for creating Monte Carlo simulation studies using R. International Journal of Mathematics and Computational Science, 4 (1), 18-33.
Abonazel, M. R. (2019). Advanced statistical techniques using R: outliers and missing data, Annual Conference on Statistics, Computer Sciences and Operations Research, Vol. 54, Dec. 2019, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.
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