132
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Kernel estimation of regression function gradient

ORCID Icon, &
Pages 135-151 | Received 30 Jul 2018, Accepted 01 Oct 2018, Published online: 31 Dec 2018

References

  • Chacón, J. E., and T. Duong. 2013. Data-driven density derivative estimation, with applications to nonparametric clustering and bump hunting. Electronic Journal of Statistics 7:499–532.
  • Chacón, J. E., T. Duong, and M. P. Wand. 2011. Asymptotics for general multivariate kernel density derivative estimators. Statistica Sinica 21 (2):807–40.
  • Chiu, S. 1990. Why bandwidth selectors tend to choose smaller bandwidths, and a remedy. Biometrika 77 (1):222–6.
  • Chiu, S. 1991. Some stabilized bandwidth selectors for nonparametric regression. The Annals of Statistics 19 (3):1528–46.
  • Craven, P., and G. Wahba. 1978. Smoothing noisy data with spline functions – Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik 31 (4):377–403.
  • Droge, B. 1996. Some comments on cross-validation (Tech. Rep. No. 1994-7). Humboldt Universitaet Berlin. http://ideas.repec.org/p/wop/humbsf/1994-7.html.
  • Fan, J. 1993. Local linear regression smoothers and their minimax efficiencies. The Annals of Statistics 21 (1):196–216.
  • Goldenshluger, A., and O. Lepski. 2011. Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality. The Annals of Statistics 39 (3):1608–32. https://hal.archives-ouvertes.fr/hal-01265258.
  • Härdle, W. 1990. Applied nonparametric regression. 1st ed. Cambridge: Cambridge University Press.
  • Herrmann, E., J. Engel, M. Wand, and T. Gasser. 1995. A bandwidth selector for bivariate kernel regression. Journal of the Royal Statistical Society. Series B (Methodological) 57 (1):171–80.
  • Horová, I., J. Koláček, and K. Vopatová. 2013. Full bandwidth matrix selectors for gradient kernel density estimate. Computational Statistics & Data Analysis 57 (1):364–76.
  • Koláček, J., and I. Horová. 2017. Bandwidth matrix selectors for kernel regression. Computational Statistics 32 (3):1027–46.
  • Koláček, J. 2005. Kernel Estimation of the Regression Function (in Czech) (Unpublished doctoral dissertation), Masaryk University, Brno.
  • Koláček, J. 2008. Plug-in method for nonparametric regression. Computational Statistics 23 (1):63–78.
  • Lafferty, J., and L. Wasserman. 2008. Rodeo: sparse, greedy nonparametric regression. The Annals of Statistics 36 (1):28–63.
  • Lau, G., P. L. Ooi, and B. Phoon. 1998. Fatal falls from a height: the use of mathematical models to estimate the height of fall from the injuries sustained. Forensic Science International 93 (1):33–44.
  • Manteiga, W. G., M. M. Miranda, and A. P. González. 2004. The choice of smoothing parameter in nonparametric regression through wild bootstrap. Computational Statistics & Data Analysis 47 (3):487–515.
  • Müller, H.-G. 1988. Nonparametric regression analysis of longitudinal data. New York: Springer.
  • Rice, J. 1984. Bandwidth choice for nonparametric regression. The Annals of Statistics 12(4):1215–30.
  • Ruppert, D., and M. P. Wand. 1994. Multivariate locally weighted least squares regression. The Annals of Statistics 22 (3):1346–70.
  • Simonoff, J. S. 1996. Smoothing methods in statistics. New York: Springer-Verlag.
  • Staniswalis, J. G., K. Messer, and D. R. Finston. 1993. Kernel estimators for multivariate regression. Journal of Nonparametric Statistics 3 (2):103–21.
  • Stone, M. 1974. Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society Series B-Statistical Methodology 36 (2):111–47.
  • Wand, M., and M. Jones. 1995. Kernel smoothing. London: Chapman and Hall.
  • Yang, L., and R. Tschernig. 1999. Multivariate bandwidth selection for local linear regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61 (4):793–815.
  • Zhang, X., R. D. Brooks, and M. L. King. 2009. A bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation. Journal of Econometrics 153 (1):21–32.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.