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 } } \neq - 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 { w ( z ) } \neq { -1 } , which is agreement with \Lambda CDM model .