サロゲｰトデｰタを用いた次元解析

22 References
  • IKEGUCHI Tohru
    Department of Applied Electronics, Science University of Tokyo
  • AIHARA Kazuyuki
    Department of Mathematical Engineering and Information Physics, University of Tokyo

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Other Title
  • On dimension estimates with surrogate data sets

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本稿は, 相関次元解析においてサロゲート法をどのように適用すべきかという点に関して議論している. ノイズを含む有限精度の実信号を解析する場合, サロゲート法などの統計的仮説検定の導入が解析結果の信頼性を向上させるために必要となる. サロゲート法を用いる場合, ある実情号に対する非線形特徴量をある固有の値として推定することが望ましいが, 次元解析の場合には, 一つの値をそのアトラクタの次元値とすることは危険である. そこで, 本稿では, モンテカルロ法による有意差検定を導入し, アトラクタのスケーリング特性と帰無仮説の棄却についてどのように解析すべきかを検討する.
In this paper, we propose a new strategy of estimating correlation dimensions in combination with the method of surrogate data, which is a kind of statistical control usually introduced to avoid spurious estimates of nonlinear statistics. In case of analyzing time series with the method of surrogate data, it is desirable to decide a value of estimated nonlinear statistics of the original data and surrogate data sets exactly. However, when dimensional analysis is applied to possible attractors reconstructed from real time series, it is very dangerous to decide a single value as an estimated dimension, because dimension is an index of self-similarity and therefore analyzed with its scaling property. In order to solve this difficulty, a dimension estimator algorithm and the method of surrogate data are combined by introducing Monte Carlo significance testing. As a result, an analysis of scaling properties at various resolution levels based on the method of surrogate data is realized.

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Details 詳細情報について

  • CRID
    1572824502214156032
  • NII Article ID
    110003198188
  • NII Book ID
    AN10013094
  • Text Lang
    en
  • Data Source
    • CiNii Articles

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