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KAKEN_23700341seika.pdf
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Download
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| Title |
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多次元確率分布の主要点に関する研究
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| Kana |
タジゲン カクリツ ブンプ ノ シュヨウテン ニ カンスル ケンキュウ
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Tajigen kakuritsu bunpu no shuyoten ni kansuru kenkyu
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A study on principal points of multivariate distributions
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松浦, 峻
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マツウラ, シュン
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Matsuura, Shun
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慶應義塾大学・理工学部・助教
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Research team head
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科研費研究者番号 : 70583368
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2015
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科学研究費補助金研究成果報告書
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2014
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確率分布のk個の主要点(k-principal points)とは, その確率分布に従う確率変数(ベクトル)と最も近い点との距離の2乗の期待値を最小にするk個の点の配置のことである。本研究では多次元確率分布のprincipal pointsの性質の解明と標本データからの推定問題に取り組み, 主に以下の成果を得た。(1) 主部分空間定理と呼ばれる, principal pointsが存在する範囲と主成分ベクトルが張る線形部分空間の関連性を示す定理の成立条件を従来よりも広い確率分布群に拡張した。(2) ある損失関数の下で最適性が保証されるなど, 新たなprincipal pointsの推定量をいくつか導いた。
A set of k-principal points of a distribution is a set of k points that minimizes the mean squared distance between the random variable (vector) and the nearest point. In this research, the properties and estimation of principal points of multivariate distributions were studied. The main results are the following : (1) Conditions previously obtained for a principal subspace theorem, which ensures that principal points are in a linear subspace spanned by the first several principal components, were extended to more general multivariate distributions. (2) Several new estimators of principal points, some of which are proven to be optimal under some loss function, were derived.
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研究種目 : 若手研究(B)
研究期間 : 2011～2014
課題番号 : 23700341
研究分野 : 統計科学
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| Jul 30, 2019 | | 著者,抄録 内容,アクセス条件 を変更 |
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