A Unified Theory of Confidence Regions and Testing for High-Dimensional Estimating Equations

By Matey Neykov, Yang Ning, Jun S. Liu. 2015

81 citations recorded by the source corpus.

We propose a new inferential framework for constructing confidence regions and testing hypotheses in statistical models specified by a system of high dimensional estimating equations. We construct an influence function by projecting the fitted estimating equations to a sparse direction obtained by solving a large-scale linear program. Our main theoretical contribution is to establish a unified Z-estimation theory of confidence regions for high dimensional problems. Different from existing methods, all of which require the specification of the likelihood or pseudo-likelihood, our framework is likelihood-free. As a result, our approach provides valid inference for a broad class of high dimensional constrained estimating equation problems, which are not covered by existing methods. Such examples include, noisy compressed sensing, instrumental variable regression, undirected graphical models, discriminant analysis and vector autoregressive models. We present detailed theoretical results for all these examples. Finally, we conduct thorough numerical simulations, and a real dataset analysis to back up the developed theoretical results.

Subfields: Computational Mechanics, Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, neutral): “…et al. (2011, 2014, 2015); Javanmard and Montanari (2014a,b, 2018); Van de Geer et al. (2014); Ning and Liu (2017); Chernozhukov et al. (2015); Neykov et al. (2018); Ren et al. (2015); Jankova and Van De Geer (2015, 2016, 2018); Bradic and Kolar (2017); Zhu and Bradic (2017, 2018)], which…”
Learning L2 Continuous Regression Functionals via Regularized Riesz Representers (2018, background): “…and Zhang (2014), Belloni Chernozhukov, and Wang (2014), Belloni, Chernozhukov, and Kato (2015), Javanmard and Montanari (2014a,b; 2015), van de Geer et al. (2014), Neykov et al. (2015), Ren et al. (2015), Jankova and van de Geer (2015, 2016a,b), Bradic and Kolar (2017), and Zhu and Bradic (2018).”
Double/de-biased machine learning using regularized Riesz representers (2018, background): “…Belloni et al. (2014a,b, 2015); Javanmard and Montanari (2014a,b, 2015); van de Geer et al. (2014); Ning and Liu (2014); Chernozhukov et al. (2015); Neykov et al. (2015); Ren et al. (2015); Jankova and Van De Geer (2015, 2016a,b); Bradic and Kolar (2017); Zhu and Bradic (2017b,a)], which focused…”
Granger Causality: A Review and Recent Advances (2021, methodology): “More recent work has developed asymptotically valid inference for the estimated parameters of the VAR process (Neykov et al., 2018; Zheng et al., 2019; Zhu and Liu, 2020).”
Robust Estimation of Causal Effects via High-Dimensional Covariate Balancing Propensity Score. (2018, background): “…high-dimensional inference on regression models; see Zhang & Zhang (2014), Javanmard &70 Montanari (2014), Van de Geer et al. (2014), Belloni et al. (2016), Ning & Liu (2017); Ning et al. (2017), Cai & Guo (2017), Neykov et al. (2018) Zhu & Bradic (2018), and Dukes et al. (2018), among many others.”