We present an analysis of broad emission lines observed in moderate-luminosity active galactic nuclei ( AGNs ) , typical of those found in X-ray surveys of deep fields , with the aim to test the validity of single-epoch virial black hole mass estimates . We have acquired near-infrared ( NIR ; 1.0 - 1.8 µm ) spectra of AGNs up to z \sim 1.8 in the COSMOS and Extended Chandra Deep Field-South Survey , with the Fiber Multi-Object Spectrograph ( FMOS ) mounted on the Subaru Telescope . These low-resolution ( R \sim 600 ) NIR spectra provide a significant detection of the broad H \alpha emission line that has been shown to be a reliable probe of black hole mass at low redshift . Our sample has existing optical spectroscopy ( through programs such as zCOSMOS ) which provides a detection of Mg ii , a broad emission line typically used for black hole mass estimation at z \gtrsim 1 . We carry out a spectral-line fitting procedure using both H \alpha and Mg ii to determine the virial velocity of gas in the broad line region , the monochromatic continuum luminosity at 3000 Å , and the total H \alpha line luminosity . With a sample of 43 AGNs spanning a range of two decades in luminosity ( i.e. , \lambda L _ { \lambda } \sim 10 ^ { 44 - 46 } ergs s ^ { -1 } ) , we find a tight correlation between the rest-frame ultraviolet and emission-line luminosity with a distribution characterized by \langle \log ( \lambda L _ { 3000 } / L _ { H \alpha } ) \rangle = 1.52 and a dispersion \sigma = 0.16 . There is also a close one-to-one relationship between the FWHM of H \alpha and of Mg ii up to 10000 km s ^ { -1 } with a dispersion of 0.14 in the distribution of the logarithm of their ratios . Both of these then lead to there being very good agreement between H \alpha - and Mg ii-based masses over a wide range in black hole mass ( i.e. , M _ { BH } \sim 10 ^ { 7 - 9 } M _ { \odot } ) . We do find a small offset in Mg ii-based masses , relative to those based on H \alpha , of +0.17 dex and a dispersion \sigma = 0.32 . In general , these results demonstrate that local scaling relations , using Mg ii or H \alpha , are applicable for AGN at moderate luminosities and up to z \sim 2 .