  Mateos et al. (2012) presented a highly reliable and efficient mid-infrared
(MIR) colour-based selection technique for luminous active galactic nuclei
(AGN) using the Wide-field Infrared Survey Explorer (WISE) survey. Here we
evaluate the effectiveness of this technique to identify obscured AGN missed in
X-ray surveys. To do so we study the WISE properties of AGN independently
selected in hard X-ray and optical surveys. We use the largest catalogue of 887
[O III]{\lambda}5007-selected type 2 quasars (QSO2s) at z<0.83 in the
literature from the Sloan Digital Sky Survey, and the 258 hard (>4.5 keV)
X-ray-selected AGN from the Bright Ultrahard XMM-Newton Survey (BUXS). The
fraction of SDSS QSO2s in our infrared AGN selection region (wedge) increases
with the AGN luminosity, reaching 66.1+4.5_4.7% at the highest [O III]
luminosities in the sample. This fraction is substantially lower than for the
BUXS type 1 AGN (96.1+3.0_6.3%), but consistent, within the uncertainties, with
that for the BUXS type 2 AGN (75.0+14.1_19.1%) with the same luminosity. The
SDSS QSO2s appear to reside in more luminous (massive) hosts than the BUXS AGN,
due to the tight magnitude limits applied in the SDSS spectroscopic target
selection. Since host galaxy dilution can reduce substantially the
effectiveness of MIR-based techniques, this may explain the lower fraction of
SDSS QSO2s in the WISE AGN wedge. The fraction of SDSS QSO2s identified as
Compton-thick candidates that fall in the wedge is consistent with the fraction
of all SDSS QSO2s in that zone. At the AGN luminosities involved in the
comparison, Compton-thick and Compton-thin SDSS QSO2s have similar WISE colour
distributions. We conclude that at high luminosities and z<1 our MIR technique
is very effective at identifying both Compton-thin and Compton-thick AGN.
