Linear Regression 金融模型中用到最多的统计工具,大概就是线性回归了。因为金融数据的噪声比较大,所以这种简单,方差小的模型更合适。 参考: https://ocw.mit.edu/courses/mathematics/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/lecture-notes/MIT18_S096F13_lecnote6.pdfocw.mit....
有直接解法:求导,令导数为零 求解过程见cs229 Lecture notes,使用Matrix derivatives和trace operator简化了运算 比较喜欢这句"Armed with the tools of matrix derivatives, let us now proceed to find in closed-form the value of θ that minimizes J (θ)." 最终得到normal equations: 如果 可逆,有如下解:...
机器学习(二)——线性回归(Linear Regression) 原文:http://cs229.stanford.edu/notes/cs229-notes1.pdf 为了使我们的住宅更有趣,我们可以考虑一个稍微更丰富的数据集,我们也知道每个房间的卧室数量: 此处的输入特征 xx 是一个在 R2R2 空间的二维向量,例如 x(i)1x1(i) 就是训练集中第 ii 个房... ...
Show mathematically why it won’t be a problemin this specific setup (see lecture notes ”Part 2 - Linear Regression”).Q3 - Non-Normality and Non-Linearity Let’s simulate a sample of n = 3000, keeping the same parameters, but adding kurtosis and skewnessto the error terms:6n = 3000X...
(2006). Using linear regression models to analyse the effect of software process improvement. Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, (pp. 234-248). Holanda.Joost Schalken,Sjaak Brinkkemper,HansVan Vliet.UsingLinear Regression Models to Analyse the Effect of ...
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Chatterjee, S., Mächler, M.: Robust regression: a weighted least squares approach, Commun. Stat. Theory Methods 26(6), 1381–1394 (1997) CrossRef Carol, J.R.: Adapting for heteroscedasticity in linear models. Ann. Stat. 10(4), 1224–1233 (1982) CrossRef Davidson, R., Flachaire...
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Linear regression: h(x)=∑i=0dθixi x0=1 d: number of input variables θi:parametersdecide how tomapXtoY 如果模型确定,即function结构确定,则主要任务转换为找一组参数θ Given a training set, learnparametersθto makeh(x)close toy 怎么定义close或者怎么衡量h(x)和y之间的距离?Cost functionJ(...