  Broad emission lines of active galactic nuclei stem from a spatially extended
region (broad-line region, BLR) that is composed of discrete clouds and
photoionized by the central ionizing continuum. The temporal behaviors of these
emission lines are blurred echoes of the continuum variations (i.e.,
reverberation mapping, RM) and directly reflect the structures and kinematic
information of BLRs through the so-called transfer function (also known as the
velocity-delay map). Based on the previous works of Rybicki & Press (1992) and
Zu et al. (2011), we develop an extended, non-parametric approach to determine
the transfer function for RM data, in which the transfer function is expressed
as a sum of a family of relatively displaced Gaussian response functions.
Therefore, arbitrary shapes of transfer functions associated with complicated
BLR geometry can be seamlessly included, enabling us to relax the presumption
of a specified transfer function frequently adopted in previous studies and to
let it be determined by observation data. We formulate our approach in a
previously well-established framework that incorporates the statistical
modeling of the continuum variations as a damped random walk process and takes
into account the long-term secular variations which are irrelevant to RM
signals. The Application to RM data shows the fidelity of our approach.
