時空間データに対する統計モデルの構築とその推定・検定について

时空数据统计模型的构建及其估计/测试

• 批准号: 09J09237
• 负责人: 平野 敏弘
• 金额: $ 0.77万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09J09237/
• 关键词: 統計学; 空間統計学; クリギング; Covariance Tapering; transformed random field; エルミート多項式; 対数正規確率場; 空間統計; 空間データ解析; 大規模データ

時空間データに対する代表的な予測方法としてクリギングが挙けられる.クリギングを行う場合,得られたサンプルの分散共分散行列の逆行列を計算する必要がある.この計算量はサンプル数nの3乗のオーダーとなるが,環境統計の分野ではサンプル数が非常に大きくなる場合があるので大規模時空間データに対するクリギングの計算量は膨大となる.この計算負荷を軽減するためにCovariance Taperingという手法が提案されている.この手法は正規確率場においては妥当であるが,降水量やコバルト濃度などの大規模空間データは通常正値を取り,データに対して対数正規分布を仮定することがあるため,これらのデータに対する適用についての理論的妥当性は不明であった,この問題に対処するため,昨年度はCovariance Taperingの対数正規確率場への拡張を行い様々な理論的結果を得た.今年度はCovariance Taperingの研究を継続し,対数正規確率場を含むようなより一般的な確率場において最適な非線形予測量,BLUP.Covariance Taperingを行ったBLUPの3つがMSEの意味で漸近的に同等であることを証明した.上記の理論的成果はdiscussion paperにまとめられ,現在投稿中である.また,一般化最小二乗推定量について,得られた時空間データの規模が大きい場合,式中に含まれる分散共分散行列の逆行列の計算負荷が極めて大きくなるので,その高速計算について考察を行い代替的な推定量を提案した.具体的には,separableな空間相関を持つ確率場の下で,doubly geometric processを真の相関構造と見なしているpseudo best estimatorを提案し,その漸近分散を導出した.提案した推定量は逆行列の計算をする必要がないので高速計算が可能である.

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项目成果

Covariance tapering for prediction of large spatial data sets

用于预测大型空间数据集的协方差锥化

• 发表时间: 2010
• 作者: Mukesh Kumar;Takahiro Sakaguchi;Fumio Koyama;矢島美寛・平野敏弘;Toshihiro Hirano;Toshihiro Hirano;平野敏弘;Toshihiro Hirano
• 通讯作者: Toshihiro Hirano

Covariance Tapering for Prediction of Large Spatial Data Sets in Transformed Random Fields

用于预测变换随机场中大型空间数据集的协方差锥化

• 发表时间: 2011
• 作者: Mukesh Kumar;Takahiro Sakaguchi;Fumio Koyama;矢島美寛・平野敏弘;Toshihiro Hirano
• 通讯作者: Toshihiro Hirano

時空間大規模データに対する統計的解析法

大规模时空数据统计分析方法

• 发表时间: 2012
• 期刊: 統計数理
• 作者: Mukesh Kumar;Takahiro Sakaguchi;Fumio Koyama;矢島美寛・平野敏弘
• 通讯作者: 矢島美寛・平野敏弘

Covariance Tapering for Prediction of Large Spatial Data Sets in Log-Gaussian Random Fields

对数高斯随机场中大型空间数据集预测的协方差锥化

• 发表时间: 2010
• 作者: Mukesh Kumar;Takahiro Sakaguchi;Fumio Koyama;矢島美寛・平野敏弘;Toshihiro Hirano;Toshihiro Hirano
• 通讯作者: Toshihiro Hirano