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Engineering estimates of methane emissions from natural gas production have led to varied projections of national emissions. This work reports direct measurements of methane emissions at 190 onshore natural gas sites in the United States (150 production sites, 27 well completion flowbacks, 9 well unloadings, and 4 workovers). For well completion flowbacks, which clear fractured wells of liquid to allow gas production, methane emissions ranged from 0.01 Mg to 17 Mg (mean = 1.7 Mg; 95% confidence bounds of 0.67–3.3 Mg), compared with an average of 81 Mg per event in the 2011 EPA national emission inventory from April 2013. Emission factors for pneumatic pumps and controllers as well as equipment leaks were both comparable to and higher than estimates in the national inventory. Overall, if emission factors from this work for completion flowbacks, equipment leaks, and pneumatic pumps and controllers are assumed to be representative of national populations and are used to estimate national emissions, total annual emissions from these source categories are calculated to be 957 Gg of methane (with sampling and measurement uncertainties estimated at ±200 Gg). The estimate for comparable source categories in the EPA national inventory is ∼1,200 Gg. Additional measurements of unloadings and workovers are needed to produce national emission estimates for these source categories. The 957 Gg in emissions for completion flowbacks, pneumatics, and equipment leaks, coupled with EPA national inventory estimates for other categories, leads to an estimated 2,300 Gg of methane emissions from natural gas production (0.42% of gross gas production).

Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation. However, a folded concave penalization problem usually has multiple local solutions and the oracle property is established only for one of the unknown local solutions. A challenging fundamental issue still remains that it is not clear whether the local optimum computed by a given optimization algorithm possesses those nice theoretical properties. To close this important theoretical gap in over a decade, we provide a unified theory to show explicitly how to obtain the oracle solution via the local linear approximation algorithm. For a folded concave penalized estimation problem, we show that as long as the problem is localizable and the oracle estimator is well behaved, we can obtain the oracle estimator by using the one-step local linear approximation. In addition, once the oracle estimator is obtained, the local linear approximation algorithm converges, namely it produces the same estimator in the next iteration. The general theory is demonstrated by using four classical sparse estimation problems, that is, sparse linear regression, sparse logistic regression, sparse precision matrix estimation and sparse quantile regression.

We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition v(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., $v \\in {H^2}(\\Omega ) \\cap H_0^1(\\Omega )$ and v ∈ L₂ (Ω). For the lumped mass method, the optimal L₂-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study.

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to all the parameters, thus providing a complete characterization of the difficulty of the estimation problem in term of the convergence rate. The lower bound is obtained by calculating the local metric entropy and an application of Fano's lemma. The rate optimal estimator is constructed using aggregation, which, however, might not be computationally feasible. We then introduce an adaptive procedure for estimating the principal subspace which is fully data driven and can be computed efficiently. It is shown that the estimator attains the optimal rates of convergence simultaneously over a large collection of the parameter spaces. A key idea in our construction is a reduction scheme which reduces the sparse PCA problem to a high-dimensional multivariate regression problem. This method is potentially also useful for other related problems.

We present the first causal estimates of the effect of Social Security Disability Insurance benefit receipt on labor supply using all program applicants. We use administrative data to match applications to disability examiners and exploit variation in examiners' allowance rates as an instrument for benefit receipt. We find that among the estimated 23 percent of applicants on the margin of program entry, employment would have been 28 percentage points higher had they not received benefits. The effect is heterogeneous, ranging from no effect for those with more severe impairments to 50 percentage points for entrants with relatively less severe impairments.

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with weighted L₁-penalty, called weighted robust Lasso (WR-Lasso), in which weights are introduced to ameliorate the bias problem induced by the L₁-penalty. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, we investigate the model selection oracle property and establish the asymptotic normality of the WR-Lasso. We show that only mild conditions on the model error distribution are needed. Our theoretical results also reveal that adaptive choice of the weight vector is essential for the WR-Lasso to enjoy these nice asymptotic properties. To make the WR-Lasso practically feasible, we propose a two-step procedure, called adaptive robust Lasso (AR-Lasso), in which the weight vector in the second step is constructed based on the L₁-penalized quantile regression estimate from the first step. This two-step procedure is justified theoretically to possess the oracle property and the asymptotic normality. Numerical studies demonstrate the favorable finite-sample performance of the AR-Lasso.

This research is the first to test the hypothesis that consumers face a “material trap” in which materialism fosters social isolation which in turn reinforces materialism. It provides evidence that materialism and loneliness are engaged in bidirectional relationships over time. Importantly, it finds that loneliness contributes more to materialism than the other way around. Moreover, it finds that materialism’s contribution to loneliness is not uniformly vicious but critically differs between specific subtypes of materialism. That is, valuing possessions as a happiness medicine or as a success measure increased loneliness, and these subtypes also increased most due to loneliness. Yet seeking possessions for material mirth decreased loneliness and was unaffected by it. These findings are based on longitudinal data from over 2,500 consumers across 6 years and a new latent growth model. They reveal how materialism and loneliness form a self-perpetuating vicious and virtuous cycle depending on the materialism subtype.

The capital-labor substitution elasticity and technical biases in production are critical parameters. The received wisdom claims their joint identification is infeasible. We challenge that interpretation. Putting the new approach of \"normalized\" production functions at the heart of a Monte Carlo analysis we identify the conditions under which identification is feasible and robust. The key result is that jointly modeling the production function and first-order conditions is superior to single-equation approaches especially when merged with \"normalization.\" Our results will have fundamental implications for production-function estimation under non-neutral technical change, for understanding the empirical relevance of normalization and variability underlying past empirical studies.

Increased adoption of the systems approach to biological research has focused attention on the use of quantitative models of biological objects. This includes a need for realistic three-dimensional (3D) representations of plant shoots for quantification and modeling. Previous limitations in single-view or multiple-view stereo algorithms have led to a reliance on volumetric methods or expensive hardware to record plant structure. We present a fully automatic approach to image-based 3D plant reconstruction that can be achieved using a single low-cost camera. The reconstructed plants are represented as a series of small planar sections that together model the more complex architecture of the leaf surfaces. The boundary of each leaf patch is refined using the level-set method, optimizing the model based on image information, curvature constraints, and the position of neighboring surfaces. The reconstruction process makes few assumptions about the nature of the plant material being reconstructed and, as such, is applicable to a wide variety of plant species and topologies and can be extended to canopy-scale imaging. We demonstrate the effectiveness of our approach on data sets of wheat (Triticum aestivum) and rice (Oryza sativa) plants as well as a unique virtual data set that allows us to compute quantitative measures of reconstruction accuracy. The output is a 3D mesh structure that is suitable for modeling applications in a format that can be imported in the majority of 3D graphics and software packages.

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank–Nicolson method. Error estimates in the L2(D)- and Hα/2(D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.