We present a systematic search for molecular hydrogen absorption systems at high redshift in quasar spectra from the Sloan Digital Sky Survey ( SDSS ) II Data Release 7 and SDSS-III Data Release 9 .
We have selected candidates using a modified profile fitting technique taking into account that the Ly \alpha forest can effectively mimic H _ { 2 } absorption systems at the resolution of SDSS data .
To estimate the confidence level of the detections , we use two methods : a Monte-Carlo sampling and an analysis of control samples .
The analysis of control samples allows us to define regions of the spectral quality parameter space where H _ { 2 } absorption systems can be confidently identified .
We find that H2 absorption systems with column densities \log { N _ { H _ { 2 } } } > 19 can be detected in only less than 3 % of SDSS quasar spectra .
We estimate the upper limit on the detection rate of saturated H _ { 2 } absorption systems ( \log { N _ { H _ { 2 } } } > 19 ) in Damped Ly- \alpha ( DLA ) systems to be about 7 % .
We provide a sample of 23 confident H _ { 2 } absorption system candidates that would be interesting to follow up with high resolution spectrographs .
There is a 1 \sigma r - i color excess and non-significant A _ { V } extinction excess in quasar spectra with an H _ { 2 } candidate compared to standard DLA-bearing quasar spectra .
The equivalent widths ( EWs ) of C ii , Si ii and Al iii ( but not Fe ii ) absorptions associated with H _ { 2 } candidate DLAs are larger compared to standard DLAs .
This is probably related to a larger spread in velocity of the absorption lines in the H _ { 2 } bearing sample .