拟合优度
拟合优度（英語：goodness of fit）描述了统计模型中对一组观测值的拟合程度。拟合优度的度量通常总结观察值与相关模型下预期值之间的差异。这些措施可用于统计假设检验，例如检验残差的正态性，检验两个样本是否来自相同的分布（参见柯尔莫哥洛夫-斯米尔诺夫检验），或者结果频率是否遵循指定的分布（参见皮尔逊卡方检验）。用某分布或分布族刻画给定数据是否合适的程度就是拟合优度，其检验方法就是拟合优度检验[1]。
在方差分析中，方差被划分成的分量之一可能是失拟平方和。对于拟合优度常见检测方法有：
参考资料
- ^ 杨振海、程维虎、张军舰. 拟合优度检验 2011年3月第一版. 北京: 科学出版社. 2010.
- ^ 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.
- ^ 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
. doi:10.1214/16-EJS1172.
- ^ 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]. （原始内容存档于2020-08-01）.
- ^ 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]. （原始内容存档于2020-02-17）.
- ^ 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. （原始内容存档 (PDF)于2018-11-23）.
