  The traditional method of computing singular value decomposition (SVD) of a
data matrix is based on a least squares principle, thus, is very sensitive to
the presence of outliers. Hence the resulting inferences across different
applications using the classical SVD are extremely degraded in the presence of
data contamination (e.g., video surveillance background modelling tasks, etc.).
A robust singular value decomposition method using the minimum density power
divergence estimator (rSVDdpd) has been found to provide a satisfactory
solution to this problem and works well in applications. For example, it
provides a neat solution to the background modelling problem of video
surveillance data in the presence of camera tampering. In this paper, we
investigate the theoretical properties of the rSVDdpd estimator such as
convergence, equivariance and consistency under reasonable assumptions. Since
the dimension of the parameters, i.e., the number of singular values and the
dimension of singular vectors can grow linearly with the size of the data, the
usual M-estimation theory has to be suitably modified with concentration bounds
to establish the asymptotic properties. We believe that we have been able to
accomplish this satisfactorily in the present work. We also demonstrate the
efficiency of rSVDdpd through extensive simulations.
