The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered by least squares minimization under nuclear norm plus l 1 norm penalization. This paper proposes a new estimator of that family based on an additional least-squares re-optimization step aimed at un-shrinking the eigenvalues of the low rank component estimated at the first step. We prove that such unshrinkage causes the final estimate to approach the target as closely as possible in Frobenius norm while recovering exactly the underlying low rank and sparsity pattern. Consistency is guaranteed when n is at least O(p 3 2 δ ), provided that the maximum number of non-zeros per row in the sparse component is O(p δ ) with δ ≤ 1 2 . Consistent recovery is ensured if the latent eigenvalues scale to p α , α ∈ [0, 1], while rank consistency is ensured if δ ≤ α. The resulting estimator is called UNALCE (UNshrunk ALgebraic Covariance Estimator) and is shown to outperform state of the art estimators, especially for what concerns fitting properties and sparsity pattern detection. The effectiveness of UNALCE is highlighted on a real example regarding ECB banking supervisory data.
A black and a white target are displayed, in five different conditions, on five grey backgrounds having different degrees of brightness (from very bright to very dark). The results show that the target having the higher contrast with its background is perceived as the nearer. With the off-white background, e.g., the black target appears as the nearer to the observer. This contradicts the well-known concept according to which the brighter target should in any case be perceived as the nearer ("relative brightness" cue). The conclusion is that the frame of reference must be taken into consideration: study of the indicators to distance in an empty space and per se is not sufficient.
The research was designed to investigate the moderating effect of some personality traits on subjective distress caused by daily hassles. The traits were internal locus of control, repression, ego strength, and barrier (as studied and defined by S. Fisher). The last two variables were negatively correlated both with the somatic and emotional distress indications and with the frequency of hassles reportED; internal locus of control showed an inverse relationship only with frequency of hassles. The hypothesis is formulated that ego strength and barrier are personality factors influencing not only the outcomes of coping (ie the stress response), but also event appraisal.
Three experiments are described on induced motion in the third dimension. In experiment 1 two constant lines on a sheet of glass appear to move in depth as a consequence of the rapid displacements of a back surface (real inducing motion); this apparent motion is the more evident (i) the longer the inspection time and (ii) the faster the inducing stimulus. In experiment 2 a constant circle appears to move in depth as a consequence of the stroboscopic displacement of a surrounding circle (apparent inducing motion). Experiment 3 compares this last induced-motion effect with the aftereffect. The importance of a dynamic frame of reference is stressed.
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