Nearly optimal minimax estimator for high-dimensional sparse linear regression

We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic factor of the optimal for any design matrix. Then by utilizing a semi-definite programming relaxation technique developed in [SIAM J. Comput. 36 (2007) 1764-1776], we obtain an approximation algorithm for computing the minimax risk for any such estimation task and also a polynomial time nearly optimal estimator for the important case of $\ell_1$ sparsity constraint. Such results were only known before for special cases, despite decades of studies on this problem. We also extend the method to the adaptive case when the parameter radius is unknown.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1141 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A systematic study of effects of stellar rotation, age spread and binaries on color-magnitude diagrams with extended main-sequence turn-offs

Stellar rotation, age spread and binary stars are thought to be three most possible causes of the peculiar color-magnitude diagrams (CMDs) of some star clusters, which exhibit extended main-sequence turn-offs (eMSTOs). It is far from getting a clear answer. This paper studies the effects of three above causes on the CMDs of star clusters systematically. A rapid stellar evolutionary code and a recently published database of rotational effects of single stars have been used, via an advanced stellar population synthesis technique. As a result, we find a consistent result for rotation to recent works, which suggests that rotation is able to explain, at least partially, the eMSTOs of clusters, if clusters are not too old ($<$ 2.0\,Gyr). In addition, an age spread of 200 to 500\,Myr reproduces extended turn-offs for all clusters younger than 2.5\,Gyr, in particular, for those younger than 2.2\,Gyr. Age spread also results in extended red clumps (eRCs) for clusters younger than 0.5\,Gyr. The younger the clusters, the clearer the eRC structures. Moreover, it is shown that binaries (including interactive binaries) affect the spread of MSTO slightly for old clusters, but they can contribute to the eMSTOs of clusters younger than 0.5\,Gyr. Our result suggests a possible way to disentangle the roles of stellar rotation and age spread, i.e., checking the existence of CMDs with both eMSTO and eRC in clusters younger than 0.5\,Gyr.Comment: Accepted to publish in ApJ

Journal Staff

There are fewer longitudinal studies from China on symptoms as described for the sick building syndrome (SBS). Here, we performed a two-year prospective study and investigated associations between environmental parameters such as room temperature, relative air humidity (RH), carbon dioxide (CO2), nitrogen dioxide (NO2), sulphur dioxide (SO2), ozone (O-3), particulate matter (PM10), and health outcomes including prevalence, incidence and remission of SBS symptoms in junior high schools in Taiyuan, China. Totally 2134 pupils participated at baseline, and 1325 stayed in the same classrooms during the study period (2010-2012). The prevalence of mucosal symptoms, general symptoms and symptoms improved when away from school (school-related symptoms) was 22.7%, 20.4% and 39.2%, respectively, at baseline, and the prevalence increased during follow-up (P&lt;0.001). At baseline, both indoor and outdoor SO2 were found positively associated with prevalence of school-related symptoms. Indoor O-3 was shown to be positively associated with prevalence of skin symptoms. At follow-up, indoor PM10 was found to be positively associated with new onset of skin, mucosal and general symptoms. CO2 and RH were positively associated with new onset of mucosal, general and school-related symptoms. Outdoor SO2 was positively associated with new onset of skin symptoms, while outdoor NO2 was positively associated with new onset of skin, general and mucosal symptoms. Outdoor PM10 was found to be positively associated with new onset of skin, general and mucosal symptoms as well as school-related symptoms. In conclusion, symptoms as described for SBS were commonly found in school children in Taiyuan City, China, and increased during the two-year follow-up period. Environmental pollution, including PM10, SO2 and NO2, could increase the prevalence and incidence of SBS and decrease the remission rate. Moreover, parental asthma and allergy (heredity) and pollen or pet allergy (atopy) can be risk factors for SBS