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  1. Abstract

    With continued fossil‐fuel dependence, anthropogenic aerosols over South Asia are projected to increase until the mid‐21st century along with greenhouse gases (GHGs). Using the Community Earth System Model (CESM1) Large Ensemble, we quantify the influence of aerosols and GHGs on South Asian seasonal precipitation patterns over the 21st century under a very high‐emissions (RCP 8.5) trajectory. We find that increasing local aerosol concentrations could continue to suppress precipitation over South Asia in the near‐term, delaying the emergence of precipitation increases in response to GHGs by several decades in the monsoon season and a decade in the post‐monsoon season. Emergence of this wetting signal is expected in both seasons by the mid‐21st century. Our results demonstrate that the trajectory of local aerosols together with GHGs will shape near‐future precipitation patterns over South Asia. Therefore, constraining precipitation response to different trajectories of both forcers is critical for informing near‐term adaptation efforts.

  2. Summary

    Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l  1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear whether corresponding estimators exist or are even computable, or if they actually yield correct partial correlation graphs. We propose a new pseudolikelihood-based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths. In particular, we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms. The objective is then optimized via a co-ordinatewise approach. The specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees; an important property that cannot be established by using standard results, when the dimension is larger than the sample size, as is often the case in high dimensional applications. These convergence guarantees ensuremore »that estimators are well defined under very general conditions and are always computable. In addition, the approach yields estimators that have good large sample properties and also respect symmetry. Furthermore, application to simulated and real data, timing comparisons and numerical convergence is demonstrated. We also present a novel unifying framework that places all graphical pseudolikelihood methods as special cases of a more general formulation, leading to important insights.

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  3. Summary

    Estimation of high dimensional covariance matrices is known to be a difficult problem, has many applications and is of current interest to the larger statistics community. In many applications including the so-called ‘large p, small n’ setting, the estimate of the covariance matrix is required to be not only invertible but also well conditioned. Although many regularization schemes attempt to do this, none of them address the ill conditioning problem directly. We propose a maximum likelihood approach, with the direct goal of obtaining a well-conditioned estimator. No sparsity assumptions on either the covariance matrix or its inverse are imposed, thus making our procedure more widely applicable. We demonstrate that the proposed regularization scheme is computationally efficient, yields a type of Steinian shrinkage estimator and has a natural Bayesian interpretation. We investigate the theoretical properties of the regularized covariance estimator comprehensively, including its regularization path, and proceed to develop an approach that adaptively determines the level of regularization that is required. Finally, we demonstrate the performance of the regularized estimator in decision theoretic comparisons and in the financial portfolio optimization setting. The approach proposed has desirable properties and can serve as a competitive procedure, especially when the sample size ismore »small and when a well-conditioned estimator is required.

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