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Articles

Adaptive local polynomial estimations for heterogeneously variational regression functions

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Pages 605-622 | Received 27 Aug 2019, Accepted 10 Sep 2020, Published online: 24 Sep 2020

References

  • Eubank RL. Nonparametric regression and spline smoothing. Boca Raton: CRC Press; 1999.
  • Fan J, Gijbels I. Local polynomial modelling and its applications. London: Chapman & Hall; 1996.
  • Green PJ, Silverman BW. Nonparametric regression and generalized linear models. London: Chapman & Hall; 1994.
  • Hastie T, Tibshirani R, Friedman J. The elements of statistical learning. New York: Springer-Verlag; 2001.
  • Ruppert D, Wand MP, Carroll RJ. Semiparametric regression. New York: Cambridge University Press; 2003.
  • Scholkopf B, Smola AJ. Learning with kernels: support vector machines, regularization, optimization, and beyond. Massachusetts: MIT Press; 2002.
  • Wahba G. Spline models for observational data. Philadelphia: SIAM; 1990.
  • Steinwart I, Christmann A. Support vector machines. New York: Springer; 2008.
  • Cleveland WS. Robust locally weighted regression and smoothing scatterplots. J Am Stat Assoc. 1979;74:829–836.
  • Fan J. Design-adaptive nonparametric regression. J Am Stat Assoc. 1992;87:998–1004.
  • Fan J. Local linear regression smoothers and their minimax efficiencies. Ann Stat. 1993;21:196–216.
  • Stone CJ. Consistent nonparametric regression. Ann Stat. 1977;5:595–620.
  • Stone CJ. Optimal rates of convergence for nonparametric estimators. Ann Stat. 1980;8:1348–1360.
  • Stone CJ. Optimal global rates of convergence for nonparametric regression. Ann Stat. 1982;10:1040–1053.
  • Geller J, Neumann MH. Improved local polynomial estimation in time series regression. J Nonparametr Stat. 2018;30:1–27.
  • Huang LS, Chan KS. Local polynomial and penalized trigonometric series regression. Stat Sin. 2014;24:1215–1238.
  • Wang W, Lin L. Derivative estimation based on difference sequence via locally weighted least squares regression. J Mach Learn Res. 2015;16:2617–2641.
  • Zhang ZG, Chan SC. On kernel selection of multivariate local polynomial modelling and its application to image smoothing and reconstruction. J Signal Process Syst. 2011;64:361–374.
  • Brabanter KD, Cao F, Gijbels I, et al. Local polynomial regression with correlated errors in random design and unknown correlation structure. Biometrika. 2018;105:681–690.
  • Cleveland WS, Devlin SJ. Locally weighted regression: an approach to regression analysis by local fitting. J Am Stat Assoc. 1988;83:596–610.
  • Fan J, Gijbels I. Data-driven bandwidth selection in local polynomial fitting: variable bandwidth and spatial adaptation. J R Stat Soc B. 1995;57:371–394.
  • Doksum K, Peterson D, Samarov A. On variable bandwidth selection in local polynomial regression. J R Stat Soc B. 2000;62:431–448.
  • Prewitt K, Lohr S. Bandwidth selection in local polynomial regression using eigenvalues. J R Stat Soc B. 2006;68:135–154.
  • Zhang ZG, Chan SC, Ho KL, et al. On bandwidth selection in local polynomial regression analysis and its application to multi-resolution analysis of non-uniform data. J Signal Process Syst. 2008;52:263–280.
  • Murthy AS, Sreenivas TV. Adaptive window for local polynomial regression from noisy nonuniform samples. In: 16th European Signal Processing Conference (EUSIPCO 2008); 2008 Aug 25–29; Lausanne, Switzerland. 2008.
  • Yang L, Hong Y. Adaptive penalized splines for data smoothing. Comput Stat Data Anal. 2017;108:70–83.
  • Takezawa K. Introduction to nonparametric regression. New Jersey: John Wiley & Sons; 2006.
  • Ruppert D, Wand MP. Multivariate locally weighted least squares regression. Ann Stat. 1994;22:1346–1370.
  • Maltamo M, Kangas A. Methods based on k-nearest neighbor regression in the prediction of basal area diameter distribution. Can J For Res. 1998;28:1107–1115.
  • Ruppert D, Sheather SJ, Wand MP. An effective bandwidth selector for local least squares regression. J Am Stat Assoc. 1995;90:1257–1270.

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