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

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著者

    • AYANO Takanori
    • Department of Mathematics, Graduate School of Science, Osaka University

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

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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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