The reconstruction of dark energy with Ridge Regression Approach
  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 $\Delta \overline w (z) = \overline
{\left| {1 + w(z)} \right|} <=0.05$ 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 $\Delta \overline w (z) = \overline {\left| {1 + w(z)}
\right|} > 0.05$, 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
$\Lambda CDM$ model.
