如何理解基于F检验的lmfit置信区间 [英] How to understand F-test based lmfit confidence intervals

问题描述

出色的lmfit程序包使您可以运行非线性回归.它可以报告两个不同的conf间隔-一个基于协方差矩阵，另一个使用基于F检验的更复杂的技术.详细信息可以在文档中找到.我想深入了解他在这项技术背后的推理.我应该阅读哪些主题?注意:我有足够的统计知识

The excellent lmfit package lets one to run nonlinear regression. It can report two different conf intervals - one based on the covarience matrix the other using a more sophisticated tecnique based on an F-test. Details can be found on the doc. I would like to understand he reasoning behind this technique in depth. Which topics should i read about? Note: i have sufficient stats knowledge

推荐答案

F统计信息和其他用于获取置信区间的相关方法要远远优于对非线性模型(和其他模型)的te co方差矩阵进行简单估计.

F stats and other associated methods for obtaining confidence intervals are far superior to a simple estimation of te co variance matrix for non-linear models (and others).

主要原因是在使用这些方法时缺乏对错误的高斯性质的假设.对于非线性系统，置信区间可以(不一定)是不对称的.这意味着参数值可以对误差表面产生不同的影响，因此，一个，两个或三个sigma极限从最佳拟合的任一方向上具有不同的大小.

The primary reason for this is the lack of assumptions about the Gaussian nature of error when using these methods. For non-linear systems, confidence intervals can (they don't have to be) be asymmetric. This means that the parameter value can effect the error surface differently and therefore the one, two, or three sigma limits have different magnitudes in either direction from the best fit.

分析型超速离心社区中有涉及错误分析的出色文章(Tom Laue，John J. Correia，Jim Cole，Peter Schuck是一些文章搜索的好名字).如果您想全面了解正确的错误分析，请查看Michael Johnson的这篇文章: http://www.researchgate.net/profile/Michael_Johnson53/publication/5881059_Nonlinear_least-squares_fitting_methods/links/0deec534d0d97a13a8000000.pdf

The analytical ultracentrifugation community has excellent articles involving error analysis (Tom Laue, John J. Correia, Jim Cole, Peter Schuck are some good names for article searches). If you want a good general read about proper error analysis, check out this article by Michael Johnson: http://www.researchgate.net/profile/Michael_Johnson53/publication/5881059_Nonlinear_least-squares_fitting_methods/links/0deec534d0d97a13a8000000.pdf

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