Penalized Composite Quasi-Likelihood for Ultrahigh-Dimensional Variable Selection

In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a data-driven weighted linear combination of convex loss functions, together with weighted $L_1$-penalty. It is completely data-adaptive and does not require prior knowledge of the error distribution. The weighted $L_1$-penalty is used both to ensure the convexity of the penalty term and to ameliorate the bias caused by the $L_1$-penalty. In the setting with dimensionality much larger than the sample size, we establish a strong oracle property of the proposed method that possesses both the model selection consistency and estimation efficiency for the true non-zero coefficients. As specific examples, we introduce a robust method of composite L1-L2, and optimal composite quantile method and evaluate their performance in both simulated and real data examples

Expected high energy emission from GRB 080319B and origins of the GeV emission of GRBs 080514B, 080916C and 081024B

We calculate the high energy (sub-GeV to TeV) prompt and afterglow emission of GRB 080319B that was distinguished by a naked-eye optical flash and by an unusual strong early X-ray afterglow. There are three possible sources for high energy emission: the prompt optical and $\gamma$-ray photons IC scattered by the accelerated electrons, the prompt photons IC scattered by the early external reverse-forward shock electrons, and the higher band of the synchrotron and the synchrotron self-Compton emission of the external shock. There should have been in total {hundreds} high energy photons detectable for the Large Area Telescope (LAT) onboard the Fermi satellite, and {tens} photons of those with energy $> 10$ GeV. The $> 10$ GeV emission had a duration about twice that of the soft $\gamma$-rays. AGILE could have observed these energetic signals if it was not occulted by the Earth at that moment. The physical origins of the high energy emission detected in GRB 080514B, GRB 080916C and GRB 081024B are also discussed. These observations seem to be consistent with the current high energy emission models.Comment: Accepted for publication in MNRAS, the interpretation of GRB 080916C has been extended, main conclusions are unchange

On the Distribution of the Adaptive LASSO Estimator

We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results in consistent model selection. We show that the finite-sample as well as the large-sample distributions are typically highly non-normal, regardless of the choice of the tuning parameter. The uniform convergence rate is also obtained, and is shown to be slower than $n^{-1/2}$ in case the estimator is tuned to perform consistent model selection. In particular, these results question the statistical relevance of the `oracle' property of the adaptive LASSO estimator established in Zou (2006). Moreover, we also provide an impossibility result regarding the estimation of the distribution function of the adaptive LASSO estimator.The theoretical results, which are obtained for a regression model with orthogonal design, are complemented by a Monte Carlo study using non-orthogonal regressors.Comment: revised version; minor changes and some material adde

Activation of Egr-1 expression in astrocytes by HIV-1 Tat: new insights into astrocyte-mediated Tat neurotoxicity

Human immunodeficiency virus type 1 (HIV-1) Tat plays an important role in HIV-associated neuropathogenesis; the underlying mechanisms are still evolving. We have recently shown that HIV-1 Tat induces expression of glial fibrillary acidic protein (GFAP), a characteristic of HIV-1 infection of the central nervous system (CNS). We have also shown that the Tat-induced GFAP expression in astrocytes is regulated by p300, and that deletion of the early growth response 1 (Egr-1) cis-transacting element within the p300 promoter abolishes Tat-induced GFAP expression. In this study, we further examined the relationship between Tat and Egr-1 in astrocytes. We found increased Egr-1 protein expression in Tat-expressing human astrocytoma cells and mouse primary astrocytes. Using the Egr-1 promoter-driven firefly luciferase reporter gene assay and the site-directed mutagenesis, we demonstrated that Tat increased Egr-1 expression by transactivating the Egr-1 promoter and involving specific serum response elements (SRE) within the promoter. Consistent with these data, we showed that Tat transactivation of the Egr-1 promoter was abrogated when astrocytes were cultured in serum-reduced media. Taken together, these results reveal that Tat directly transactivates Egr-1 expression and suggest that Tat interaction with Egr-1 is probably one of the very upstream molecular events that initiate Tat-induced astrocyte dysfunction and subsequent Tat neurotoxicity