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1. High-dimensional empirical likelihood inference

   https://doi.org/10.1093/biomet/asaa051  

   Chang, Jinyuan ; Chen, Song Xi ; Tang, Cheng Yong ; Wu, Tong Tong ( October 2020 , Biometrika)

   null (Ed.)

   Summary High-dimensional statistical inference with general estimating equations is challenging and remains little explored. We study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications tests. First, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. Second, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. Numerical studies demonstrate promising performance and potential practical benefits of the new methods. 

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2. A Regularization-Based Adaptive Test for High-Dimensional Generalized Linear Models

   Wu, C ; Xu, G ; Shen, X. Pan ( June 2020 , Journal of machine learning research)

   In spite of its urgent importance in the era of big data, testing high-dimensional parameters in generalized linear models (GLMs) in the presence of high-dimensional nuisance parameters has been largely under-studied, especially with regard to constructing powerful tests for general (and unknown) alternatives. Most existing tests are powerful only against certain alternatives and may yield incorrect Type I error rates under high-dimensional nuisance parameter situations. In this paper, we propose the adaptive interaction sum of powered score (aiSPU) test in the framework of penalized regression with a non-convex penalty, called truncated Lasso penalty (TLP), which can maintain correct Type I error rates while yielding high statistical power across a wide range of alternatives. To calculate its p-values analytically, we derive its asymptotic null distribution. Via simulations, its superior finite-sample performance is demonstrated over several representative existing methods. In addition, we apply it and other representative tests to an Alzheimer’s Disease Neuroimaging Initiative (ADNI) data set, detecting possible gene-gender interactions for Alzheimer’s disease. We also put R package “aispu” implementing the proposed test on GitHub. 

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3. Simultaneous Selection and Inference for Varying Coefficients with Zero Regions: A Soft-Thresholding Approach

   https://doi.org/10.1111/biom.13900  

   Yang, Yuan ; Pan, Ziyang ; Kang, Jian ; Brummett, Chad ; Li, Yi ( July 2023 , Biometrics)

   Varying coefficient models have been used to explore dynamic effects in many scientific areas, such as in medicine, finance, and epidemiology. As most existing models ignore the existence of zero regions, we propose a new soft-thresholded varying coefficient model, where the coefficient functions are piecewise smooth with zero regions. Our new modeling approach enables us to perform variable selection, detect the zero regions of selected variables, obtain point estimates of the varying coefficients with zero regions, and construct a new type of sparse confidence intervals that accommodate zero regions. We prove the asymptotic properties of the estimator, based on which we draw statistical inference. Our simulation study reveals that the proposed sparse confidence intervals achieve the desired coverage probability. We apply the proposed method to analyze a large-scale preoperative opioid study.

    

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4. Counterfactual Sensitivity and Robustness

   https://doi.org/10.3982/ECTA17232  

   Christensen, Timothy ; Connault, Benjamin ( January 2023 , Econometrica)

   We propose a framework for analyzing the sensitivity of counterfactuals to parametric assumptions about the distribution of latent variables in structural models. In particular, we derive bounds on counterfactuals as the distribution of latent variables spans nonparametric neighborhoods of a given parametric specification while other “structural” features of the model are maintained. Our approach recasts the infinite‐dimensional problem of optimizing the counterfactual with respect to the distribution of latent variables (subject to model constraints) as a finite‐dimensional convex program. We also develop an MPEC version of our method to further simplify computation in models with endogenous parameters (e.g., value functions) defined by equilibrium constraints. We propose plug‐in estimators of the bounds and two methods for inference. We also show that our bounds converge to the sharp nonparametric bounds on counterfactuals as the neighborhood size becomes large. To illustrate the broad applicability of our procedure, we present empirical applications to matching models with transferable utility and dynamic discrete choice models. 

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5. Debiased machine learning of global and local parameters using regularized Riesz representers

   https://doi.org/10.1093/ectj/utac002  

   Chernozhukov, Victor ; Newey, Whitney K. ; Singh, Rahul ( April 2022 , The Econometrics Journal)

   We provide adaptive inference methods, based on $\ell _1$ regularization, for regular (semiparametric) and nonregular (nonparametric) linear functionals of the conditional expectation function. Examples of regular functionals include average treatment effects, policy effects, and derivatives. Examples of nonregular functionals include average treatment effects, policy effects, and derivatives conditional on a covariate subvector fixed at a point. We construct a Neyman orthogonal equation for the target parameter that is approximately invariant to small perturbations of the nuisance parameters. To achieve this property, we include the Riesz representer for the functional as an additional nuisance parameter. Our analysis yields weak ‘double sparsity robustness’: either the approximation to the regression or the approximation to the representer can be ‘completely dense’ as long as the other is sufficiently ‘sparse’. Our main results are nonasymptotic and imply asymptotic uniform validity over large classes of models, translating into honest confidence bands for both global and local parameters.

    

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