2000 Fiscal Year Annual Research Report

複雑非線形現象の統計理論の開発と応用

Research Project

Project/Area Number	09440083
Research Institution	KYUSHU UNIVERSITY
Principal Investigator	柳川堯九州大学, 大学院・数理学研究院, 教授 (80029488)
Co-Investigator(Kenkyū-buntansha)	大瀧慈広島大学, 原爆放射能医学研究所, 教授 (20110463) 田栗正章千葉大学, 理学部, 教授 (10009607) 小西貞則九州大学, 大学院・数理学研究院, 教授 (40090550) 笛田薫九州大学, 大学院・数理学研究院, 助手 (50253399) 柿沢佳秀北海道大学, 大学院・経済学研究科, 助教授 (30281778)
Keywords	ブートストラップ法 / 超過分散 / 一般化非線形モデル / 観測カオス / 情報量基準 / 非線形自己回帰モデル / 離散多変量データ / リアプノフ指数
Research Abstract	・観測カオス時系列データから埋め込み次元と遅れ時間を推定する方法を開発し、脈波データおよび脳波データに適用し、開発した方法の有効性を実証した. ・ダイナミックノイズをもつ非線形自己回帰モデルから観測されるデータに基づいてスケルトンのリアプノフ指数を推定する方法を開発し、推定量の一致性を証明した. ・正則化法によって推定されたロジスティックモデルを評価するための規準を導出し,その有効性を実データ,シミュレーションを通して検証した. ・ベイズ型予測分布モデルの評価規準を求め,モデル評価の観点からハイパーパラメータの有効な推定法を開発した. ・ブートストラップ法を用いるノンパラメトリックな方法について、幾つかの検定方法を開発した.また、複雑な標本抽出方式における非線形の推定値の標本誤差の推定には、ブートストラップ法が極めて有効であることを実証した. ・交交替条件付き期待値アルゴリズムを開発し、ソフトウエアを開発した. ・定常時系列の枠組みで、バハドールスロープの有効性を証明した. ・予測の平均2乗誤差のクロス・バリデーション推定量の漸近正規性を示した. ・超過ポアソン変動および超過二項変動をもつ母集団に対する非線形傾向性検定を開発し、超過変動をもつ複雑な非線形反応を高い検出力で検出することを検証した. ・counter-matchingサンプリングの場合のMantel-Haenszel推定量を開発した.また、ペアワイズ条件付き推定関数を用いたMantel-Haenszel推定量の拡張を行った.

Research Products
(23 results)

All Other

All Publications (23 results)

[Publications] Zhang,Z-Z., et al.: "On Mantel-Haenszel type estimators in simple nested case-control study,"Communication in Statistics, Theory and Methods. 29-11. 2507-2521 (2000)
[Publications] Yanagawa,T. et al.: "Analysis of observed chaotic data by non-linear autoregressive model"Proceedings of the International Symposium on Frontier of Time series Modeling. 252-262 (2000)
[Publications] Yanagawa,T. et al.: "Detecting chaos in physiological data"Proceedings of An International Conference on Recent Developments in Statistics and Probability and Their Applications. 530-534 (2000)
[Publications] Zhang,Z-Z.and Yanagawa,T.: "Generalized Begun-Reid estimators for multiple hazard rates"J of Statistical Planning and Inference. (印刷中).
[Publications] Yanagawa,T.and Kikuchi,Y.: "Statistical issues on the determination of the No-Observed-Adverse-Effect levels in toxicology"Environmetrics. (印刷中).
[Publications] 小西貞則: "統計的モデリングと情報量規準"応用数理,. 10-3. 14-33 (2000)
[Publications] 小西貞則: "統計的モデリングと情報量規準構成の理論-汎関数に基づくアプローチ-"数学. 52-2. 128-141 (2000)
[Publications] Sakurai,H.and Taguri,M.: "Bootstrap test of mean difference of paired longitudinal data by curve resampling"Proceedings of the Seventh Japan-China Symposium on Statistics. 193-196 (2000)
[Publications] Hashimoto,A. et.al: "Numerical consideration on maximizing correlation coefficient under non-linear constraints"Proceedings of the Seventh Japan-China Symposium on Statistics. 383-384 (2000)
[Publications] Hashimoto,A. et al.: "On optimal solusions under quadratic constraints"Proceedings of the Tenth Japan and Korea Joint Conference of Statistics : Statistical Prediction and Computing. 203-208 (2000)
[Publications] Sakurai,H.and Taguri,M.: "Bootstrap tests for the equality of two regression functions by curve resampling"Abstract of Intnatl Conf on Statist, Combi and Related Areas and the Seventh Intnatl Conf of the Forum for Interdisciplinary Math. 54-54 (2000)
[Publications] Taguri,M. et al.: "On the problem of maximizing correlation under quadratic constraint"Abstract of Intnatl Conf on Statist, Combi and Related Areas and the Seventh Intnatl Conf of the Forum for Interdisciplinary Math. 67-67 (2000)
[Publications] Sakurai,H.and Taguri,M.: "Bootstrap tests for mean difference of paired data with dependency : Comparison of the sizes and powers by simulation,"Journal of Statistical Computation and Simulation. (印刷中).
[Publications] Kakizawa,Y.: "On Bahadur asympotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes"Stochastic Processes and their Applications. 85-1. 29-44 (2000)
[Publications] Kakizawa,Y.: "Local comparison of Rao and Wald statistics in the Bahadur sense."Statistica Sinica. 10-1. 297-315 (2000)
[Publications] 濱崎俊光他: "ベキ変換とその変型"応用統計学. 25. 357-381 (2000)
[Publications] Nakayama,T. et al.: "Statistical analysis of female proportion among the Japanese infant population of 0-4 year olds"Jpn J of Biometrics.. 20. 155-166 (2000)
[Publications] 高橋綾他: "戸建て住宅の価格と環境条件に関するノンパラメトリック"広島女学院大学生活科学部紀要. 7. 57-65 (2000)
[Publications] 大瀧慈他: "治療効果における固体変動を考慮した多変量生存時間データ解析法の開発"がん治療のあゆみ、. 19. 17-24 (2000)
[Publications] Ohtaki,M.and Niwa,O.: "Mathematical implications for radiation carcinogenesis based on hypothesis of induction of genomic instability"Jpn J Biometrics,. 21-1. 77-84 (2000)
[Publications] Kawasaki,H. et al.: "Statistical analysis of geographical features oflung cancer mortality in Japan"Jpn J of Clinical Oncology. 30. 557-561 (2000)
[Publications] Fueda,K.and Yanagawa,T.: "Estimating the embedding dimension and delay time from chaotic time series with dynamic noise"J of the Japan Statistical Society. (印刷中).
[Publications] Taniguchi,M.and Kakizawa,Y.: "Asymptotic Theory of Statistical Inference for Time Series"Springer. 385 (2000)

2000 Fiscal Year Annual Research Report

複雑非線形現象の統計理論の開発と応用

Principal Investigator

柳川 堯 九州大学, 大学院・数理学研究院, 教授 (80029488)

Research Products

[Publications] Zhang,Z-Z., et al.: "On Mantel-Haenszel type estimators in simple nested case-control study,"Communication in Statistics, Theory and Methods. 29-11. 2507-2521 (2000)

[Publications] Yanagawa,T. et al.: "Analysis of observed chaotic data by non-linear autoregressive model"Proceedings of the International Symposium on Frontier of Time series Modeling. 252-262 (2000)

[Publications] Yanagawa,T. et al.: "Detecting chaos in physiological data"Proceedings of An International Conference on Recent Developments in Statistics and Probability and Their Applications. 530-534 (2000)

[Publications] Zhang,Z-Z.and Yanagawa,T.: "Generalized Begun-Reid estimators for multiple hazard rates"J of Statistical Planning and Inference. (印刷中).

[Publications] Yanagawa,T.and Kikuchi,Y.: "Statistical issues on the determination of the No-Observed-Adverse-Effect levels in toxicology"Environmetrics. (印刷中).

[Publications] 小西貞則: "統計的モデリングと情報量規準"応用数理,. 10-3. 14-33 (2000)

[Publications] 小西貞則: "統計的モデリングと情報量規準構成の理論-汎関数に基づくアプローチ-"数学. 52-2. 128-141 (2000)

[Publications] Sakurai,H.and Taguri,M.: "Bootstrap test of mean difference of paired longitudinal data by curve resampling"Proceedings of the Seventh Japan-China Symposium on Statistics. 193-196 (2000)

[Publications] Hashimoto,A. et.al: "Numerical consideration on maximizing correlation coefficient under non-linear constraints"Proceedings of the Seventh Japan-China Symposium on Statistics. 383-384 (2000)

[Publications] Hashimoto,A. et al.: "On optimal solusions under quadratic constraints"Proceedings of the Tenth Japan and Korea Joint Conference of Statistics : Statistical Prediction and Computing. 203-208 (2000)

[Publications] Sakurai,H.and Taguri,M.: "Bootstrap tests for the equality of two regression functions by curve resampling"Abstract of Intnatl Conf on Statist, Combi and Related Areas and the Seventh Intnatl Conf of the Forum for Interdisciplinary Math. 54-54 (2000)

[Publications] Taguri,M. et al.: "On the problem of maximizing correlation under quadratic constraint"Abstract of Intnatl Conf on Statist, Combi and Related Areas and the Seventh Intnatl Conf of the Forum for Interdisciplinary Math. 67-67 (2000)

[Publications] Sakurai,H.and Taguri,M.: "Bootstrap tests for mean difference of paired data with dependency : Comparison of the sizes and powers by simulation,"Journal of Statistical Computation and Simulation. (印刷中).

[Publications] Kakizawa,Y.: "On Bahadur asympotic efficiency of the maximum likelihood and quasi-maximum likelihood estimators in Gaussian stationary processes"Stochastic Processes and their Applications. 85-1. 29-44 (2000)

[Publications] Kakizawa,Y.: "Local comparison of Rao and Wald statistics in the Bahadur sense."Statistica Sinica. 10-1. 297-315 (2000)

[Publications] 濱崎俊光 他: "ベキ変換とその変型"応用統計学. 25. 357-381 (2000)

[Publications] Nakayama,T. et al.: "Statistical analysis of female proportion among the Japanese infant population of 0-4 year olds"Jpn J of Biometrics.. 20. 155-166 (2000)

[Publications] 高橋綾 他: "戸建て住宅の価格と環境条件に関するノンパラメトリック"広島女学院大学生活科学部紀要. 7. 57-65 (2000)

[Publications] 大瀧慈 他: "治療効果における固体変動を考慮した多変量生存時間データ解析法の開発"がん治療のあゆみ、. 19. 17-24 (2000)

[Publications] Ohtaki,M.and Niwa,O.: "Mathematical implications for radiation carcinogenesis based on hypothesis of induction of genomic instability"Jpn J Biometrics,. 21-1. 77-84 (2000)

[Publications] Kawasaki,H. et al.: "Statistical analysis of geographical features oflung cancer mortality in Japan"Jpn J of Clinical Oncology. 30. 557-561 (2000)

[Publications] Fueda,K.and Yanagawa,T.: "Estimating the embedding dimension and delay time from chaotic time series with dynamic noise"J of the Japan Statistical Society. (印刷中).

[Publications] Taniguchi,M.and Kakizawa,Y.: "Asymptotic Theory of Statistical Inference for Time Series"Springer. 385 (2000)

柳川堯九州大学, 大学院・数理学研究院, 教授 (80029488)

[Publications] 濱崎俊光他: "ベキ変換とその変型"応用統計学. 25. 357-381 (2000)

[Publications] 高橋綾他: "戸建て住宅の価格と環境条件に関するノンパラメトリック"広島女学院大学生活科学部紀要. 7. 57-65 (2000)

[Publications] 大瀧慈他: "治療効果における固体変動を考慮した多変量生存時間データ解析法の開発"がん治療のあゆみ、. 19. 17-24 (2000)