In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.

It is now widely accepted that volatility models have to incorporate the so-called leverage effect in order to to model the dynamics of daily financial returns. We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. We derive the asymptotic properties of the quasi-maximum likelihood estimator of the parameters. These properties are established both when the power of the transformation is known or is unknown. The asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed. Introduction The ARCH (AutoRegressive Conditional Heteroscedastic) model has been introduced by Engle (1982) in an univariate context. Since this work a lot of extensions have been proposed. A first one has been suggested four years latter, namely the GARCH (Generalised ARCH) model by Bollerslev (1986). This model had for goal to improve modeling by considering the past conditional variance (volatility). Their concept are based on the past conditional heteroscedasticity which depends on the past values of the return. A consequence is the volatility has the same magnitude for a negative or positive return. Financial series have their own characteristics which are usually difficult to reproduce artificially. An important characteristic is the leverage effect which consider negative returns differently than the positive returns. This is in contradiction with the construction of the GARCH model, because it cannot consider the asymmetry. The TGARCH (Threshold GARCH) model introduced by Rabemananjara and Zakoïan (1993) improve modeling because it considers the asymmetry since the volatility is determined by the past negative observations and the past positive observations with different weights. Various asymmetric GARCH processes are introduced in the econometric literature, for instance the EGARCH (Exponential GARCH) and the log GARCH models (see Francq et al. (2013) who studied the asymptotic properties of an EGARCH (1, 1) models).

A message passing algorithm is derived for recovering a dense subgraph within a graph generated by a variation of the Barab\'asi-Albert preferential attachment model. The estimator is assumed to know the arrival times, or order of attachment, of the vertices. The derivation of the algorithm is based on belief propagation under an independence assumption. Two precursors to the message passing algorithm are analyzed: the first is a degree thresholding (DT) algorithm and the second is an algorithm based on the arrival times of the children (C) of a given vertex, where the children of a given vertex are the vertices that attached to it. Algorithm C significantly outperforms DT, showing it is beneficial to know the arrival times of the children, beyond simply knowing the number of them. For fixed fraction of vertices in the community, fixed number of new edges per arriving vertex, and fixed affinity between vertices in the community, the probability of error for recovering the label of a vertex is found as a function of the time of attachment, for either algorithm DT or C, in the large graph limit. By averaging over the time of attachment, the limit in probability of the fraction of label errors made over all vertices is identified, for either of the algorithms DT or C.