  This work analyzes the subspace-constrained Tyler's estimator (STE) designed
for recovering a low-dimensional subspace within a dataset that may be highly
corrupted with outliers. It assumes a weak inlier-outlier model and allows the
fraction of inliers to be smaller than a fraction that leads to computational
hardness of the robust subspace recovery problem. It shows that in this
setting, if the initialization of STE, which is an iterative algorithm,
satisfies a certain condition, then STE can effectively recover the underlying
subspace. It further shows that under the generalized haystack model, STE
initialized by the Tyler's M-estimator (TME), can recover the subspace when the
fraction of iniliers is too small for TME to handle.
