论文标题
通过山脊回归方法重建暗能量
The reconstruction of dark energy with Ridge Regression Approach
论文作者
论文摘要
如果暗能随时间发展，则可以通过非参数法确定。 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.我们获得了初步测试结果，该结果表明$δ\ edline w（z）= \ overline {\ left | {1 + w（z）} \ right |} <= 0.05 $包括$ w（z）= -1 $，在测试中，$ {w_ {concon}} \ ne -1 $对$ {w_ {concon}}} \ ne -1 $造成I型I错误的可能性为零（$ 1 \％$）；否则，如果$δ\ editelline w（z）= \ + edline {\ left | {1 + w（z）} \ right |}> 0.05 $，对于$ {w_ {conse}} = -1 $不超过$ 10 \％$的$ {w_ {conse}} = -1 $的概率。最后，我们使用JLA示例重建$ W（z）$，结果拒绝$ {\ rm {w（z）}}} \ ne {\ rm { - 1}} $，与$λcdm$模型一致。
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.
