Rates of convergence for nearest neighbor estimators with the smoother regression function

Takanori Ayano

doi:10.1016/j.jspi.2012.03.012

Rates of convergence for nearest neighbor estimators with the smoother regression function

Statistics Theory 2025-12-23 v1 Statistics Theory

Authors: Takanori Ayano

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Abstract

In regression analysis one wants to estimate the regression function from a data. In this paper we consider the rate of convergence for the nearest neighbor estimator in case that the regression function is $(p,C)$ -smooth. It is an open problem whether the optimal rate can be achieved by some nearest neighbor estimator in case that $p$ is on (1,1.5]. We solve the problem affirmatively. This is the main result of this paper. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected $L_2$ error.

Keywords

nearest neighbor estimator rate of convergence regression function smoothness expected L2 error nonparametric regression

Cite

@article{arxiv.1102.5633,
  title  = {Rates of convergence for nearest neighbor estimators with the smoother regression function},
  author = {Takanori Ayano},
  journal= {arXiv preprint arXiv:1102.5633},
  year   = {2025}
}

Comments

12 pages, 1 table

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