Testing and Confidence Intervals for High Dimensional Proportional Hazards Models

Fang, Ethan X.; Ning, Yang; Liu, Han

doi:10.1111/rssb.12224

Cited by 69 publications

(99 citation statements)

References 40 publications

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“…In principle, the inference problem for many high dimensional models can be analyzed by using the current framework, although the technical details can be different case by case; see Ning and Liu (2014); Fang et al (2014). Similar to many existing procedures (Belloni et al, 2013;Zhang and Zhang, 2011;van de Geer et al, 2014;Javanmard and Montanari, 2013), the construction of the score function depends on the tuning parameters λ and λ .…”

Section: Discussionmentioning

confidence: 99%

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

Ning

Liu²

2017

Ann. Statist.

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256

327

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We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our approach provides a general framework for high dimensional inference and is applicable to a wide range of applications. From the testing perspective, we develop general theorems to characterize the limiting distributions of the decorrelated score test statistic under both null hypothesis and local alternatives. These results provide asymptotic guarantees on the type I errors and local powers of the proposed test. Furthermore, we show that the decorrelated score function can be used to construct point estimators that are semiparametrically efficient and the optimal confidence regions. We also generalize this framework to broaden its applications. First, we extend it to handle high dimensional null hypothesis, where the number of parameters of interest can increase exponentially fast with the sample size. Second, we establish the theory for model misspecification. Third, we go beyond the likelihood framework, by introducing the generalized score test based on general loss functions. Thorough numerical studies are conducted to back up the developed theoretical results.

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Section: Discussionmentioning

confidence: 99%

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

Ning

Liu²

2017

Ann. Statist.

Self Cite

256

327

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“…The sparsity Assumption 2 ensures that the LASSO selector converges to the true value at a fast rate. A similar assumption has been made in Fang et al (2016). Under Assumption 3, at most c 3 ≤ c 1 c 2 parameters are needed to fully determine the distributions of X k , Z j , and ϵ.…”

Section: Asymptotic Resultsmentioning

confidence: 98%

Inference for Low-Dimensional Covariates in a High-Dimensional Accelerated Failure Time Model

et al. 2019

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Data with high-dimensional covariates are now commonly encountered. Compared to other types of responses, research on high-dimensional data with censored survival responses is still relatively limited. In addition, most of the existing studies have been focused on estimation and variable selection. In this study, we consider data with a censored survival response, a set of low-dimensional covariates of main interest, and a set of high-dimensional covariates that may also affect survival. The accelerated 1 Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) failure time model is adopted to describe survival. The goal is to conduct inference for the effects of low-dimensional covariates, while properly accounting for the highdimensional covariates. A penalization-based procedure is developed, and its validity is established under mild and widely adopted conditions. Simulation suggests satisfactory performance of the proposed procedure, and the analysis of two cancer genetic datasets demonstrates its practical applicability.

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“…For the rest of this section, we explain the assumptions and theoretical results needed for Theorem 2 summarized in Lemmas 3-7. Condition (D1) is needed whenever the model departs significantly from the linear case (van de Geer et al, 2014;Fang et al, 2017). In our case, the asymptotic normality of √ nṁ(β o ) depends fundamentally on the asymptotic tightness of √ n˙ m(β o ).…”

Section: Asymptotic Normality For One-step Estimator and Honest Covermentioning

confidence: 96%

Inference under Fine-Gray competing risks model with high-dimensional covariates

Hou¹,

Bradić²,

Xu³

2019

Electron. J. Statist.

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The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biomedical applications, a high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literature. We fill in this gap by developing confidence intervals based on a one-step bias-correction for a regularized estimation. We develop a theoretical framework for the partial likelihood, which does not have independent and identically distributed entries and therefore presents many technical challenges. We also study the approximation error from the weighting scheme under random censoring for competing risks and establish new concentration results for time-dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.MSC 2010 subject classifications: Primary 62N03, 62F30; secondary 62J07.

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Testing and Confidence Intervals for High Dimensional Proportional Hazards Models

Cited by 69 publications

References 40 publications

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

Inference for Low-Dimensional Covariates in a High-Dimensional Accelerated Failure Time Model

Inference under Fine-Gray competing risks model with high-dimensional covariates

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