Marginal empirical likelihood and sure independence feature screening

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically examined, and we find that the marginal empirical likelihood ratio evaluated at zero can be used to differentiate whether an explanatory variable is contributing to a response variable or not. Based on this finding, we propose a unified feature screening procedure for linear models and the generalized linear models. Different from most existing feature screening approaches that rely on the magnitudes of some marginal estimators to identify true signals, the proposed screening approach is capable of further incorporating the level of uncertainties of such estimators. Such a merit inherits the self-studentization property of the empirical likelihood approach, and extends the insights of existing feature screening methods. Moreover, we show that our screening approach is less restrictive to distributional assumptions, and can be conveniently adapted to be applied in a broad range of scenarios such as models specified using general moment conditions. Our theoretical results and extensive numerical examples by simulations and data analysis demonstrate the merits of the marginal empirical likelihood approach.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1139 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimal covariance matrix estimation for high-dimensional noise in high-frequency data

In this paper, we consider efficiently learning the structural information from the highdimensional noise in high-frequency data via estimating its covariance matrix with optimality. The problem is uniquely challenging due to the latency of the targeted high-dimensional vector containing the noises, and the practical reality that the observed data can be highly asynchronous -- not all components of the high-dimensional vector are observed at the same time points. To meet the challenges, we propose a new covariance matrix estimator with appropriate localization and thresholding. In the setting with latency and asynchronous observations, we establish the minimax optimal convergence rates associated with two commonly used loss functions for the covariance matrix estimations. As a major theoretical development, we show that despite the latency of the signal in the high-frequency data, the optimal rates remain the same as if the targeted high-dimensional noises are directly observable. Our results indicate that the optimal rates reflect the impact due to the asynchronous observations, which are slower than that with synchronous observations. Furthermore, we demonstrate that the proposed localized estimator with thresholding achieves the minimax optimal convergence rates. We also illustrate the empirical performance of the proposed estimator with extensive simulation studies and a real data analysis

Studies on FEM Geometrical Model of Gear Machined by Pre-Grinding Hob with protuberance

ABSTRACT Conjugate curves are cut by the different parts of a pre-grinding hob with protuberance, appearing in subsection nonlinearly, which makes the combined fillet curves difficult to describe with explicit equations and makes the tooth profil

Mixing layer height and its implications for air pollution over Beijing, China

The mixing layer is an important meteorological factor that affects air pollution. In this study, the atmospheric mixing layer height (MLH) was observed in Beijing from July 2009 to December 2012 using a ceilometer. By comparison with radiosonde data, we found that the ceilometer underestimates the MLH under conditions of neutral stratification caused by strong winds, whereas it overestimates the MLH when sand-dust is crossing. Using meteorological, PM$_{2.5}$, and PM$_{10}$ observational data, we screened the observed MLH automatically; the ceilometer observations were fairly consistent with the radiosondes, with a correlation coefficient greater than 0.9. Further analysis indicated that the MLH is low in autumn and winter and high in spring and summer in Beijing. There is a significant correlation between the sensible heat flux and MLH, and the diurnal cycle of the MLH in summer is also affected by the circulation of mountainous plain winds. Using visibility as an index to classify the degree of air pollution, we found that the variation in the sensible heat and buoyancy term in turbulent kinetic energy (TKE) is insignificant when visibility decreases from 10 to 5 km, but the reduction of shear term in TKE is near 70 %. When visibility decreases from 5 to 1 km, the variation of the shear term in TKE is insignificant, but the decrease in the sensible heat and buoyancy term in TKE is approximately 60 %. Although the correlation between the daily variation of the MLH and visibility is very poor, the correlation between them is significantly enhanced when the relative humidity increases beyond 80 %. This indicates that humidity-related physicochemical processes is the primary source of atmospheric particles under heavy pollution and that the dissipation of atmospheric particles mainly depends on the MLH. The presented results of the atmospheric mixing layer provide useful empirical information for improving meteorological and atmospheric chemistry models and the forecasting and warning of air pollution

Two-year continuous measurements of carbonaceous aerosols in urban Beijing, China: temporal variations, characteristics and source analyses

Organic carbon (OC) and elemental carbon (EC) in the PM2.5 of urban Beijing were measured hourly with a semi-continuous thermal-optical analyzer from Jan 1, 2013 to Dec 31, 2014. The annual average OC and EC concentrations in Beijing were 17.0 ± 12.4 and 3.4 ± 2.0 μg/m3 for 2013, and 16.8 ± 14.5 and 3.5 ± 2.9 μg/m3 for 2014. It is obvious that the annual average concentrations of OC and EC in 2014 were not less than those in 2013 while the annual average PM2.5 concentration (89.4 μg/m3) in 2014 was slightly reduced as compared to that (96.9 μg/m3) in 2013. Strong seasonality of the OC and EC concentrations were found with high values during the heating seasons and low values during the non-heating seasons. The diurnal cycles of OC and EC characterized by higher values at night and in the morning were caused by primary emissions, secondary transformation and stable meteorological condition. Due to increasing photochemical activity, the OC peaks were observed at approximately noon. No clear weekend effects were observed. Interestingly, in the early mornings on weekends in the autumn and winter, the OC and EC concentrations were close to or higher than those on weekdays. Our data also indicate that high OC and EC concentrations were closely associated with their potential source areas which were determined based on the potential source contribution function analysis. High potential source areas were identified and were mainly located in the south of Beijing and the plain of northern China. A much denser source region was recorded in the winter than in the other seasons, indicating that local and regional transport over regional scales are the most important. These results demonstrate that both regional transport from the southern regions and local accumulation could lead to the enhancements of OC and EC and likely contribute to the severe haze pollution in Beijing

Highly time-resolved chemical characterization and implications of regional transport for submicron aerosols in the North China Plain

To investigate the regional transport and formation mechanisms of submicron aerosols in the North China Plan (NCP), for the first time, we conducted simultaneous combined observations of the non-refractory submicron aerosols (NR-PM1) chemical compositions using aerosol mass spectrometer at urban Beijing (BJ) and at regional background area of the NCP (XL), from November 2018 to January 2019. During the observation period, average mass concentrations of PM1 in BJ and XL were 26.6 +/- 31.7 and 16.0 +/- 18.7 mu g m(-3) respectively. The aerosol composition in XL showed a lower contribution of organic aerosol (33% vs. 43%) and higher fractions of nitrate (35% vs. 30%), ammonium (16% vs. 13%), and chlorine (2% vs. 1%) than in BJ. Additionally, a higher contribution of secondary organic aerosol (SOA) was also observed in XL, suggesting low primary emissions and highly oxidized OA in the background area. Nitrate displayed a significantly enhanced contribution with the aggravation of aerosol pollution in both BJ and XL, which was completely neutralized by excess ammonium at both sites, that the abundant ammonia emissions in the NCP favor nitrate formation on a regional scale. In addition, a higher proportion of nitrate in XL can be attributed to the more neutral and higher oxidation capacity of the background atmosphere. Heterogeneous aqueous reaction plays an important role in sulfate and SOA formation, and is more efficient in BJ which can be attributed to the higher aerosol surface areas at urban site. Regional transport from the southwestern regions of NCP showed a significant impact on the formation of haze episodes. Beside the invasion of transported pollutants, the abundant water vapor associated with the air mass to the downwind background area further enhanced local secondary transformation and expanded the regional scope of the haze pollution in the NCP. (C) 2019 Elsevier B.V. All rights reserved.Peer reviewe