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擬合優度

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擬合優度(英語:goodness of fit)描述了統計模型中對一組觀測值的擬合程度。擬合優度的度量通常總結觀察值與相關模型下預期值之間的差異。這些措施可用於統計假設檢驗,例如檢驗殘差的正態性,檢驗兩個樣本是否來自相同的分布(參見柯爾莫哥洛夫-斯米爾諾夫檢驗),或者結果頻率是否遵循指定的分布(參見皮爾遜卡方檢驗)。用某分布或分布族刻畫給定數據是否合適的程度就是擬合優度,其檢驗方法就是擬合優度檢驗[1]

在方差分析中,方差被劃分成的分量之一可能是失擬平方和。對於擬合優度常見檢測方法有:

參考資料

  1. ^ 楊振海、程維虎、張軍艦. 拟合优度检验 2011年3月第一版. 北京: 科學出版社. 2010. 
  2. ^ Berk, Robert H.; Jones, Douglas H. Goodness-of-fit test statistics that dominate the Kolmogorov statistics. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete. 1979, 47 (1): 47–59. doi:10.1007/BF00533250. 
  3. ^ Moscovich, Amit; Nadler, Boaz; Spiegelman, Clifford. On the exact Berk-Jones statistics and their p-value calculation. Electronic Journal of Statistics. 2016, 10 (2). arXiv:1311.3190可免費查閱. doi:10.1214/16-EJS1172. 
  4. ^ Liu, Qiang; Lee, Jason; Jordan, Michael. A Kernelized Stein Discrepancy for Goodness-of-fit Tests. Proceedings of the 33rd International Conference on Machine Learning. The 33rd International Conference on Machine Learning. New York, New York, USA: Proceedings of Machine Learning Research: 276–284. 20 June 2016 [2023-10-13]. (原始內容存檔於2020-08-01). 
  5. ^ Chwialkowski, Kacper; Strathmann, Heiko; Gretton, Arthur. A Kernel Test of Goodness of Fit. Proceedings of the 33rd International Conference on Machine Learning. The 33rd International Conference on Machine Learning. New York, New York, USA: Proceedings of Machine Learning Research: 2606–2615. 20 June 2016 [2023-10-13]. (原始內容存檔於2020-02-17). 
  6. ^ Zhang, Jin. Powerful goodness-of-fit tests based on the likelihood ratio (PDF). J. R. Stat. Soc. B. 2002, 64 (2): 281–294 [5 November 2018]. doi:10.1111/1467-9868.00337. (原始內容存檔 (PDF)於2018-11-23).