基于岭回归方法的暗能量重构
The reconstruction of dark energy with Ridge Regression Approach
AI总结：
本研究提出结合PCA与岭回归有偏估计的暗能量重构方法，搭配新主成分选择准则和拉格朗日插值积分方法，测试显示其I类错误率低，用JLA样本重构w(z)的结果符合ΛCDM模型。
摘要：
暗能量是否随时间演化可通过非参数方法判定。我们提出一种在岭回归分析基础上结合主成分分析（PCA）与有偏估计的参数重构方法，同时提出一种新颖的主成分选择准则以避免主成分选取的随意性，并采用拉格朗日插值数值积分将近平坦空间中的光度距离积分公式线性化，以避免函数数据求导的不稳定性。我们得到初步测试结果：若$Δ\
英文摘要：
It may be determined by non-parametric method if the dark energy evolves with time. We propose a method of combining PCA and biased estimation on the basis of ridge regression analysis to reconstruct parameters, meanwhile we present an interesting principal component selection criterion to avoid the arbitrariness of principal component selections, and use numerical integral by Lagrange interpolation to linearize the luminosity distance integral formula in nearly flat space to avoid instability of derivative for functional data. We get the preliminary test results that shows if $Δ\overline w (z) = \overline {\left| {1 + w(z)} \right|} <=0.05$ included $w(z) = -1$, the probability of making a type I error for ${w_{recon}} \ne -1$ is almost zero ($1\% $) in the test; otherwise, if $Δ\overline w (z) = \overline {\left| {1 + w(z)} \right|} > 0.05$, the probability of making a type I error for ${w_{recon}} = -1$ is not more than $10\% $. Finally, we use JLA sample to reconstruct $w(z)$, and the results reject ${\rm{w(z) }} \ne {\rm{ - 1}}$, which is agreement with $ΛCDM$ model.
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