Uncertainty Quantification Under Group Sparsity

Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical result is generalized to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.Comment: 44 page

Star Formation Properties in Barred Galaxies(SFB). III. Statistical Study of Bar-driven Secular Evolution using a sample of nearby barred spirals

Stellar bars are important internal drivers of secular evolution in disk galaxies. Using a sample of nearby spiral galaxies with weak and strong bars, we explore the relationships between the star formation feature and stellar bars in galaxies. We find that galaxies with weak bars tend to be coincide with low concentrical star formation activity, while those with strong bars show a large scatter in the distribution of star formation activity. We find enhanced star formation activity in bulges towards stronger bars, although not predominantly, consistent with previous studies. Our results suggest that different stages of the secular process and many other factors may contribute to the complexity of the secular evolution. In addition, barred galaxies with intense star formation in bars tend to have active star formation in their bulges and disks, and bulges have higher star formation densities than bars and disks, indicating the evolutionary effects of bars. We then derived a possible criterion to quantify the different stages of bar-driven physical process, while future work is needed because of the uncertainties.Comment: 30 single-column pages, 9 figures, accepted for publication in A