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

## 抄録

Let (<i>X</i>,<i>Y</i>) be a $\\mathbb{R}^d\\times\\mathbb{R}$-valued random vector. In regression analysis one wants to estimate the regression function $m(x):={\\bf E}(Y|X=x)$ from a data set. In this paper we consider the convergence rate of the error for the <i>k</i> nearest neighbor estimators in case that <i>m</i> is (<i>p</i>,<i>C</i>)-smooth. It is known that the minimax rate is unachievable by any <i>k</i> nearest neighbor estimator for <i>p</i> > 1.5 and <i>d</i>=1. We generalize this result to any <i>d</i> ≥ 1. Throughout this paper, we assume that the data is independent and identically distributed and as an error criterion we use the expected <i>L</i><sub>2</sub> error.

## 収録刊行物

• IEICE transactions on information and systems

IEICE transactions on information and systems 94(11), 2244-2249, 2011-11-01

The Institute of Electronics, Information and Communication Engineers

## 各種コード

• NII論文ID(NAID)
10030194121
• NII書誌ID(NCID)
AA10826272
• 本文言語コード
ENG
• 資料種別
ART
• ISSN
09168532
• データ提供元
CJP書誌  J-STAGE

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