High-dimensional instrumental variables regression and confidence sets

This article considers inference in linear models with d\_X regressors, some or many of which could be endogenous, and d\_Z instrumental variables (IVs). d\_Z can range from less than d\_X to any order smaller than an exponential in the sample size. For moderate d\_X, identification robust confidence sets are obtained by solving a hierarchy of semidefinite programs. For large d\_X, we propose the STIV estimator. The analysis of its error uses sensitivity characteristics introduced in this paper. Robust confidence sets are derived by solving linear programs. Results on rates of convergence, variable selection, and confidence sets which "adapt" to the sparsity are given. Generalizations include models with endogenous IVs and systems of equations with approximation errors. We also analyse confidence bands for vectors of linear functionals and functions using bias correction. The application is to a demand system with approximation errors, cross-equation restrictions, and thousands of endogenous regressors

Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images

MaxSAT Evaluation 2017 : Solver and Benchmark Descriptions

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