Advanced search
Publication Cover
Communications in Statistics - Theory and Methods Volume 44, 2015 - Issue 10
Submit an article Journal homepage
166
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

On Variance-Stabilizing Multivariate Non Parametric Regression Estimation

Kiheiji NishidaGraduate School of Medicine, Osaka University, Suita, Osaka, JapanCorrespondence[email protected]
&
Yuichiro KanazawaGraduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan
Pages 2151-2175 | Received 30 Jun 2011, Accepted 01 Feb 2013, Published online: 26 May 2015

References

  • Fan, J., Gijbels, I. (1992). Variable bandwidth and local linear regression smoothers. Ann. Stat. 20:2008–2036.
  • Fan, J., Gijbels, I. (1995). Adaptive order polynomial fitting: Bandwidth robustification and bias reduction. J. Comput. Graph. Stat. 4:213–227.
  • Fan, J., Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85:645–660.
  • Kanazawa, Y. (1992). An optimal variable cell histogram based on the sample spacings. Ann. Stat. 20:291–304.
  • Kanazawa, Y. (1993a). Hellinger distance and Akaike’s information criterion for the histogram. Stat. Prob. Lett. 17:293–298.
  • Kanazawa, Y. (1993b). Hellinger distance and Kullback-Leibler loss for the Kernel density estimator. Stat. Prob. Lett. 18:315–321.
  • Kanazawa, Y., Kogure, A., Lee, S.G. (1999). On the asymptotic equivalence of Hellinger distance and Kullback-Leibler loss. J. Jpn. Stat. Soc. 29:1–21.
  • Marron, J.S., Härdle, W. (1986). Random approximations to some measures of accuracy in nonparametric curve estimation. J. Multivariate Anal. 20:91–113.
  • Nadaraya, E.A. (1964). On estimating regression. Theor. Prob. Appl. 9:141–142.
  • Nadaraya, E.A. (1965). On nonparametric estimation of density functions and regression curves. Theor. Prob. Appl. 10:186–190.
  • Nadaraya, E.A. (1970). Remarks on nonparametric estimates for density functions and regression curves. Theor. Prob. Appl. 15:134–137.
  • Nishida, K., Kanazawa, Y. (2011). Introduction to the variance-stabilizing bandwidth for the Nadaraya-Watson regression estimator. Bull. Informat. Cybernet. 43:53–66.
  • Ruppert, D., Wand, M.P. (1994). Multivariate locally weighted least squares regression. Ann. Stat. 22:1346–1370.
  • Scott, D.W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. New YorkNY: Wiley.
  • Wand, M.P., Jones, M.C. (1993). Comparison of smoothing parametrizations in bivariate kernel density estimation. J. Amer. Stat. Assoc. 88:520–528.
  • Watson, G.S. (1964). Smooth regression analysis. Sankhy Ser. A 26:359–372.
  • Watson, G.S., Leadbetter, M.R. (1963). On the estimation of probability density. I. Ann. Math. Stat. 34:480–491.
  • Yang, L., Tschernig, R. (1999). Multivariate bandwidth selection for local linear regression. J. Royal Stat. Soc. Ser. B 61:793–815.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.