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On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size

Year 2018, Volume: 22 Issue: 2, 511 - 520, 15.08.2018

Nursel Koyuncu Muhammad Hanıf Shabnam Shahzadı Usman Shahzad

Abstract

In this paper, we studied an Adaptive Nadaraya Watson kernel estimator to check the bias effect on both side of the discontinuity in the presence of jump size for regression discontinuity model. We have proposed the modified Adaptive Nadaraya Watson kernel estimator and derived its normality and
variance. We have also compared with the asymptotic normality of the Mean Integrated Square Error (MISE) of Adaptive Nadaraya Watson kernel estimator and Nadaraya Watson kernel estimator. The results obtained from the simulation study have showed that Adaptive Nadaraya Watson estimator has better performance than the Nadaraya Watson Kernel estimator.

Keywords

Adaptive Nadaraya Watson Jump size; Mean Integrated Square Error; Rate of convergence

References

  • [1] Gao, J., Pettitt, A.N.,Wolff, R.C.L. 1998. Local Linear Kernel Estimation for Discontinuous Nonparametric Regression Function. Communication in Statistics - Theory and Methods, 27(12), 2871-2894.
  • [2] Yin, Y.Q. 1988. Detection of the Number, Locations and Magnitudes of jumps. Communication in Statistics.Stochastic Models, 4, 445-455.
  • [3] Porter, J. 1998. Estimation of Regression Discontinuities. Seminar Notes.
  • [4] Demir, S., Toktamis, O. 2010. On the Adaptive Nadaraya Watson Kernel Regression Estimators. Hacettepe Journal of Mathematics and Statistics, 39(3), 429-437.
  • [5] Hardle, W. 1990. Applied Nonparametric Regression. Cambridge University Press.
  • [6] Pangan, A., Ullah, A. 1999. Nonparametric Econometrics. Cambridge University Press, New York.
  • [7] Silverman, B. 1992. Density Estimation for Statistics and Data Analysis. Chapman and Hall, New york.
  • [8] Stone, C. 1980. Optimal Rates of Convergence for Nonparametric Estimators. The Annals of Statistics, 8, 1348-1360.
  • [9] Hahn, J., Todd, P., Klaauw, V.W. 2001. Identification and Estimation of Treatment Effects with a Regression Discontinuity Design. Econometrica , 69(1), 201-209.
  • [10] Trochim, W. 1984. Research Design for Program Evaluation; The Regression Discontinuity Approach.
  • [11] Hall, P., Schucany W. R. 1989. A Local Crossvalidation Algorithm. Statistics and Probability Letters, 8, 109-117.

Year 2018, Volume: 22 Issue: 2, 511 - 520, 15.08.2018

Nursel Koyuncu Muhammad Hanıf Shabnam Shahzadı Usman Shahzad

Abstract

References

  • [1] Gao, J., Pettitt, A.N.,Wolff, R.C.L. 1998. Local Linear Kernel Estimation for Discontinuous Nonparametric Regression Function. Communication in Statistics - Theory and Methods, 27(12), 2871-2894.
  • [2] Yin, Y.Q. 1988. Detection of the Number, Locations and Magnitudes of jumps. Communication in Statistics.Stochastic Models, 4, 445-455.
  • [3] Porter, J. 1998. Estimation of Regression Discontinuities. Seminar Notes.
  • [4] Demir, S., Toktamis, O. 2010. On the Adaptive Nadaraya Watson Kernel Regression Estimators. Hacettepe Journal of Mathematics and Statistics, 39(3), 429-437.
  • [5] Hardle, W. 1990. Applied Nonparametric Regression. Cambridge University Press.
  • [6] Pangan, A., Ullah, A. 1999. Nonparametric Econometrics. Cambridge University Press, New York.
  • [7] Silverman, B. 1992. Density Estimation for Statistics and Data Analysis. Chapman and Hall, New york.
  • [8] Stone, C. 1980. Optimal Rates of Convergence for Nonparametric Estimators. The Annals of Statistics, 8, 1348-1360.
  • [9] Hahn, J., Todd, P., Klaauw, V.W. 2001. Identification and Estimation of Treatment Effects with a Regression Discontinuity Design. Econometrica , 69(1), 201-209.
  • [10] Trochim, W. 1984. Research Design for Program Evaluation; The Regression Discontinuity Approach.
  • [11] Hall, P., Schucany W. R. 1989. A Local Crossvalidation Algorithm. Statistics and Probability Letters, 8, 109-117.
There are 11 citations in total.

Details

Journal Section Articles
Authors

Nursel Koyuncu

Muhammad Hanıf This is me

Shabnam Shahzadı This is me

Usman Shahzad

Publication Date August 15, 2018
Published in Issue Year 2018 Volume: 22 Issue: 2

Cite

APA Koyuncu, N., Hanıf, M., Shahzadı, S., Shahzad, U. (2018). On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 511-520.
AMA Koyuncu N, Hanıf M, Shahzadı S, Shahzad U. On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size. SDÜ Fen Bil Enst Der. August 2018;22(2):511-520.
Chicago Koyuncu, Nursel, Muhammad Hanıf, Shabnam Shahzadı, and Usman Shahzad. “On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, no. 2 (August 2018): 511-20.
EndNote Koyuncu N, Hanıf M, Shahzadı S, Shahzad U (August 1, 2018) On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 511–520.
IEEE N. Koyuncu, M. Hanıf, S. Shahzadı, and U. Shahzad, “On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size”, SDÜ Fen Bil Enst Der, vol. 22, no. 2, pp. 511–520, 2018.
ISNAD Koyuncu, Nursel et al. “On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (August 2018), 511-520.
JAMA Koyuncu N, Hanıf M, Shahzadı S, Shahzad U. On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size. SDÜ Fen Bil Enst Der. 2018;22:511–520.
MLA Koyuncu, Nursel et al. “On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, 2018, pp. 511-20.
Vancouver Koyuncu N, Hanıf M, Shahzadı S, Shahzad U. On the Adaptive Nadaraya-Watson Kernel Estimator for the Discontinuity in the Presence of Jump Size. SDÜ Fen Bil Enst Der. 2018;22(2):511-20.
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