The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter _<i>f</i> that is critical to the identification for consistency and propose a three-step quasi-maximum likelihood procedure with non-Gaussian likelihood functions. This novel approach is consistent and asymptotically normal under weak moment conditions. Moreover, it achieves better efficiency than the Gaussian alternative, particularly when the innovation error has heavy tails. We also summarize and compare the values of the scale parameter and the asymptotic efficiency for estimators based on different choices of likelihood functions with an increasing level of heaviness in the

We study several aspects of holographic entanglement in two models known as flat3/BMSFT and (W)AdS3/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS3 or AdS3 backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on "modular chaos" introduced recently in the context of the AdS/CFT correspondence.

The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. In [1], it was shown empirically that using lscr^p minimization with p &lt; 1 can do so with fewer measurements than with p = 1. In this paper we consider the use of iteratively reweighted algorithms for computing local minima of the nonconvex problem. In particular, a particular regularization strategy is found to greatly improve the ability of a reweighted least-squares algorithm to recover sparse signals, with exact recovery being observed for signals that are much less sparse than required by an unregularized version (such as FOCUSS, [2]). Improvements are also observed for the reweighted-lscr¹ approach of [3].

A convex speech enhancement (CSE) method is presented based on convex optimization and pause detection of the speech sources. Channel spatial difference is identified for enhancing each speech source individually while suppressing other interfering sources. Sparse unmixing filters indicating channel spatial differences are sought by <i>l</i> ₁ norm regularization and the split Bregman method. A subdivided split Bregman method is developed for efficiently solving the problem in severely reverberant environments. The speech pause detection is based on a binary mask source separation method. The CSE method is evaluated objectively and subjectively, and found to outperform a list of existing blind speech separation approaches on both synthetic and room recorded speech mixtures in terms of the overall computational speed and separation quality.

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