Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation

Shi, Chengchun; Song, Rui; Li, Runze

doi:10.1080/01621459.2019.1710154

Cited by 26 publications

(17 citation statements)

References 25 publications

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“…Following the proof of Lemma A.1 of Shi et al (2020), we have max j 1 ,j 2 , β ( ) 0 (j 1 , j 2 ) 2 = O(1). Since λ min (Σ 0 ) and λ max (Σ 0 ) are uniformly bounded away from zero and infinity, there exists some constant κ ≥ 1 such that, for any j 1 , j 2 ,…”

Section: Proof Of Lemmamentioning

confidence: 99%

Testing Mediation Effects Using Logic of Boolean Matrices

Shi

2021

Journal of the American Statistical Association

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A central question in high-dimensional mediation analysis is to infer the significance of individual mediators. The main challenge is that the total number of potential paths that go through any mediator is super-exponential in the number of mediators. Most existing mediation inference solutions either explicitly impose that the mediators are conditionally independent given the exposure, or ignore any potential directed paths among the mediators. In this article, we propose a novel hypothesis testing procedure to evaluate individual mediation effects, while taking into account potential interactions among the mediators. Our proposal thus fills a crucial gap, and greatly extends the scope of existing mediation tests. Our key idea is to construct the test statistic using the logic of Boolean matrices, which enables us to establish the proper limiting distribution under the null hypothesis. We further employ screening, data splitting, and decorrelated estimation to reduce the bias and increase the power of the test. We show that our test can control both the size and false discovery rate asymptotically, and the power of the test approaches one, while allowing the number of mediators to diverge to infinity with the sample size. We demonstrate the efficacy of the method through simulations and a neuroimaging study of Alzheimer's disease. A Python implementation of the proposed procedure is available at https://github. com/callmespring/LOGAN.

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Section: Proof Of Lemmamentioning

confidence: 99%

Testing Mediation Effects Using Logic of Boolean Matrices

Shi

2021

Journal of the American Statistical Association

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“…In this part, we evaluate the performance of our proposed method in a real dataset about riboflavin (vitamin B 2 ) production with Bacillus subtilis, which is publicly available in the R package hdi. This dataset was analyzed by Dezeure et al (2015), Yin (2017), andShi et al (2020). It consists of a single real-valued response variable which is the logarithm of the riboflavin production rate and p = 4088 predictors measuring the logarithm of the expression level of 4088 genes.…”

Section: Real Data Analysismentioning

confidence: 99%

High-Dimensional Sparse Single-Index Regression Via Hilbert-Schmidt Independence Criterion

Wu¹,

Deng²,

Chen³

2021

Preprint

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Hilbert-Schmidt Independence Criterion (HSIC) has recently been used in the field of single-index models to estimate the directions. Compared with some other well-established methods, it requires relatively weaker conditions. However, its performance has not yet been studied in the high-dimensional scenario, where the number of covariates is much larger than the sample size. In this article, we propose a new efficient sparse estimate in HSIC based single-index model. This new method estimates the subspace spanned by the linear combinations of the covariates directly and performs variable selection simultaneously. Due to the non-convexity of the objective function, we use a majorize-minimize approach together with the linearized alternating direction method of multipliers algorithm to solve the optimization problem. The algorithm does not involve the inverse of the covariance matrix and therefore can handle the large p small n scenario naturally. Through extensive simulation studies and a real data analysis, we show our proposal is efficient and effective in the high-dimensional setting. The Matlab codes for this method are available online.

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“…Our research also makes new contributions to statistical inference in high-dimensional semiparametric models. Recent work on inference has been mostly limited to linear regression or generalized linear regression, see Zhang and Zhang [2014], Van de Geer et al [2014], Javanmard and Montanari [2014], Belloni et al [2015], Cai et al [2017], Ning et al [2017], Zhang and Cheng [2017], Zhu and Bradic [2018], Shi et al [2020], among others.…”

Section: Introductionmentioning

confidence: 99%

Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension

Wu¹,

Wang

2021

Preprint

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This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate simultaneous inference to determine if a group of variables is relevant for estimating an optimal decision rule in a high-dimensional semiparametric framework. The unknown link function permits flexible modeling of the interactions between the treatment and the covariates, but leads to nonconvex estimation in high dimension and imposes significant challenges for inference. We first establish that a local restricted strong convexity condition holds with high probability and that any feasible local sparse solution of the estimation problem can achieve the near-oracle estimation error bound.

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Statistical Inference for High-Dimensional Models via Recursive Online-Score Estimation

Cited by 26 publications

References 25 publications

Testing Mediation Effects Using Logic of Boolean Matrices

Testing Mediation Effects Using Logic of Boolean Matrices

High-Dimensional Sparse Single-Index Regression Via Hilbert-Schmidt Independence Criterion

Model-Assisted Uniformly Honest Inference for Optimal Treatment Regimes in High Dimension

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