The Lower Bound for the Nearest Neighbor Estimators with (<I>p</I>,<I>C</I>)-Smooth Regression Functions

Takanori AYANO

doi:10.1587/transinf.E94.D.2244

The Lower Bound for the Nearest Neighbor Estimators with (p,C)-Smooth Regression Functions

Takanori AYANO

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Let (X,Y) be a R^d R-valued random vector. In regression analysis one wants to estimate the regression function m(x):=E(Y|X=x) from a data set. In this paper we consider the convergence rate of the error for the k nearest neighbor estimators in case that m is (p,C)-smooth. It is known that the minimax rate is unachievable by any k nearest neighbor estimator for p > 1.5 and d=1. We generalize this result to any d ≥ 1. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected L₂ error.

Publication: IEICE TRANSACTIONS on Information Vol.E94-D No.11 pp.2244-2249

Publication Date: 2011/11/01

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Online ISSN: 1745-1361

DOI: 10.1587/transinf.E94.D.2244

Type of Manuscript: PAPER

Category: Artificial Intelligence, Data Mining

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Takanori AYANO, "The Lower Bound for the Nearest Neighbor Estimators with (p,C)-Smooth Regression Functions" in IEICE TRANSACTIONS on Information, vol. E94-D, no. 11, pp. 2244-2249, November 2011, doi: 10.1587/transinf.E94.D.2244.
Abstract: Let (X,Y) be a R^d R-valued random vector. In regression analysis one wants to estimate the regression function m(x):=E(Y|X=x) from a data set. In this paper we consider the convergence rate of the error for the k nearest neighbor estimators in case that m is (p,C)-smooth. It is known that the minimax rate is unachievable by any k nearest neighbor estimator for p > 1.5 and d=1. We generalize this result to any d ≥ 1. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected L₂ error.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E94.D.2244/_p

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@ARTICLE{e94-d_11_2244,
author={Takanori AYANO, },
journal={IEICE TRANSACTIONS on Information},
title={The Lower Bound for the Nearest Neighbor Estimators with (p,C)-Smooth Regression Functions},
year={2011},
volume={E94-D},
number={11},
pages={2244-2249},
abstract={Let (X,Y) be a R^d R-valued random vector. In regression analysis one wants to estimate the regression function m(x):=E(Y|X=x) from a data set. In this paper we consider the convergence rate of the error for the k nearest neighbor estimators in case that m is (p,C)-smooth. It is known that the minimax rate is unachievable by any k nearest neighbor estimator for p > 1.5 and d=1. We generalize this result to any d ≥ 1. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected L₂ error.},
keywords={},
doi={10.1587/transinf.E94.D.2244},
ISSN={1745-1361},
month={November},}

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TY - JOUR
TI - The Lower Bound for the Nearest Neighbor Estimators with (p,C)-Smooth Regression Functions
T2 - IEICE TRANSACTIONS on Information
SP - 2244
EP - 2249
AU - Takanori AYANO
PY - 2011
DO - 10.1587/transinf.E94.D.2244
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E94-D
IS - 11
JA - IEICE TRANSACTIONS on Information
Y1 - November 2011
AB - Let (X,Y) be a R^d R-valued random vector. In regression analysis one wants to estimate the regression function m(x):=E(Y|X=x) from a data set. In this paper we consider the convergence rate of the error for the k nearest neighbor estimators in case that m is (p,C)-smooth. It is known that the minimax rate is unachievable by any k nearest neighbor estimator for p > 1.5 and d=1. We generalize this result to any d ≥ 1. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected L₂ error.
ER -