Context : Blue-shifted Fe K absorption lines have been detected in recent years between 7 and 10 keV in the X-ray spectra of several radio-quiet AGNs .
The derived blue-shifted velocities of the lines can often reach mildly relativistic values , up to 0.2–0.4c .
These findings are important because they suggest the presence of a previously unknown massive and highly ionized absorbing material outflowing from their nuclei , possibly connected with accretion disk winds/outflows .

Aims : The scope of the present work is to statistically quantify the parameters and incidence of the blue-shifted Fe K absorption lines through a uniform analysis on a large sample of radio-quiet AGNs .
This allows us to assess their global detection significance and to overcome any possible publication bias .

Methods : We performed a blind search for narrow absorption features at energies greater than 6.4 keV in a sample of 42 radio-quiet AGNs observed with XMM-Newton .
A simple uniform model composed by an absorbed power-law plus Gaussian emission and absorption lines provided a good fit for all the data sets .
We derived the absorption lines parameters and calculated their detailed detection significance making use of the classical F-test and extensive Monte Carlo simulations .

Results : We detect 36 narrow absorption lines on a total of 101 XMM-Newton EPIC pn observations .
The number of absorption lines at rest-frame energies higher than 7 keV is 22 .
Their global probability to be generated by random fluctuations is very low , less than 3 \times 10 ^ { -8 } , and their detection have been independently confirmed by a spectral analysis of the MOS data , with associated random probability < 10 ^ { -7 } .
We identify the lines as Fe XXV and Fe XXVI K-shell resonant absorption .
They are systematically blue-shifted , with a velocity distribution ranging from zero up to \sim 0.3c , with a peak and mean value at \sim 0.1c .
We detect variability of the lines on both EWs and blue-shifted velocities among different XMM-Newton observations even on time-scales as short as a few days , possibly suggesting somewhat compact absorbers .
Moreover , we find no significant correlation between the cosmological red-shifts of the sources and the lines blue-shifted velocities , ruling out any systematic contamination by local absorption .
If we define Ultra-fast Outflows ( UFOs ) those highly ionized absorbers with outflow velocities higher than 10 ^ { 4 } km/s , then the majority of the lines are consistent with being associated to UFOs and the fraction of objects with detected UFOs in the whole sample is at least \sim 35 % .
This fraction is similar for Type 1 and Type 2 sources .
The global covering fraction of the absorbers is consequently estimated to be in the range C \sim 0.4–0.6 , thereby implying large opening angles .

Conclusions : From our systematic X-ray spectral analysis on a large sample of radio-quiet AGNs we have been able to clearly assess the global veracity of the blue-shifted Fe K absorption lines at E > 7 keV and to overcome their publication bias .
These lines indicate that UFOs are a rather common phenomenon observable in the central regions of these sources and they are probably the direct signature of AGN accretion disk winds/ejecta .
The detailed photo-ionization modeling of these absorbers is presented in a companion paper .