Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1603.06663

Confidence regions for entries of a large precision matrix

Jinyuan Chang·Yumou Qiu·Qiwei Yao·Tao Zou
View original source ↗Read source document ↗Export metadata ↓

Abstract

Precision matrices play important roles in many practical applications. Motivated by temporally dependent multivariate data in modern social and scientific studies, we consider the statistical inference of precision matrices for high-dimensional time dependent observations. Specifically, we propose a data-driven procedure to construct a class of simultaneous confidence regions for the precision coefficients within an index set of interest. The confidence regions can be applied to test for specific structures of a precision matrix and to recover its nonzero components. We first construct an estimator of the underlying precision matrix via penalized node-wise regressions, and then develope the Gaussian approximation results on the maximal difference between the estimated and true precision matrices. A computationally feasible parametric bootstrap algorithm is developed to implement the proposed procedure. Theoretical results indicate that the proposed procedure works well without the second order cross-time stationary assumption on the data and sparse structure conditions on the long-run covariance of the estimates. Simulation studies and a real example on S&P 500 stock return data confirm the performance of the proposed approach.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jinyuan Chang, Yumou Qiu, Qiwei Yao, Tao Zou. 2018-03-27. Confidence regions for entries of a large precision matrix. https://doi.org/10.1016/j.jeconom.2018.03.020

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Considerations for the Integration of Randomized Controlled Trials and Real-World Data

As clinical decision-making increasingly moves toward individualized and context-specific treatment recommendations, reliance on any single evidence source, randomized or observational, may be insufficient. Principled integration of randomized controlled trials and real-world data, grounded in explicit causal frameworks, offers a path toward evidence that is both internally credible and externally relevant. In this article, we describe distinct objectives for the integration of randomized controlled trials and real-world data and discuss how these objectives shape key design and analytic considerations, illustrating the resulting choices through example estimands. We highlight practical issues that commonly arise in applied settings, including data relevance and curation, cross-source comparability, estimand specification, and sensitivity analysis. We aim for this article to help readers evaluate and implement principled approaches to integrating randomized controlled trials and real-world data in ways that can support more reliable treatment recommendations while maintaining regulatory-grade evidentiary standards.

stat.ME↗
arXiv2026

Validity of MMRM-based hypothesis testing under missing-not-at-random mechanisms

In randomized clinical trials with longitudinal continuous outcomes, missing-not-at-random (MNAR) missingness often motivates conservative alternatives to mixed models for repeated measures (MMRM). Such caution is important for estimation, but estimation and testing need not require identical assumptions. Moreover, overly conservative primary analyses may reduce power, increase required sample size, and raise trial costs. We investigated the validity of MMRM-based testing under the global null of identical longitudinal outcome distributions across groups. Because valid testing minimally requires treatment-effect estimators to converge to the null under the null hypothesis, we investigated sufficient conditions for this property. We introduced a proportional observation condition requiring ratios of observation probabilities relative to a reference group, conditional on the full outcome vector, to be outcome-independent, and showed that, with arbitrary post-baseline visits and monotone missingness, this condition is sufficient for convergence to the null value. The condition allows observation to depend on unobserved outcomes and permits between-group differences in overall observation probabilities through outcome-independent dropout, making it clinically interpretable while accommodating outcome-dependent MNAR missingness. Synthetic and data-based bootstrap simulations showed negligible bias and empirical test sizes near 0.05, including nonmonotone missingness. Thus, MNAR missingness does not by itself imply that a more conservative primary testing procedure is required. This result does not justify treatment-effect estimation under alternatives, which still requires estimand-based interpretation and sensitivity analyses.

stat.ME↗
arXiv2026

Optimized variance estimation under interference and complex experimental designs

Unbiased and consistent variance estimators generally do not exist for design-based treatment effect estimators because experimenters never observe more than one potential outcome for any unit. The problem is exacerbated by interference and complex experimental designs. Experimenters must accept conservative variance estimators in these settings, but they can strive to minimize the conservativeness. In this paper, we show that the task of constructing a minimally conservative variance estimator can be interpreted as an optimization problem that aims to find the lowest estimable upper bound of the true variance given the experimenter's risk preferences and knowledge of the potential outcomes. We characterize the set of admissible bounds in the class of quadratic forms, and we demonstrate that the optimization problem is a convex program for many natural objectives. The resulting variance estimators are guaranteed to be conservative regardless of whether the background knowledge used to construct the bound is correct, but the estimators are less conservative if the provided information is reasonably accurate. Numerical results show that the resulting variance estimators can be considerably less conservative than existing estimators, allowing experimenters to draw more informative inferences about treatment effects.

stat.ME↗