Indirect multivariate response linear regression

Molstad, Aaron J.; Rothman, Adam

doi:10.1093/biomet/asw034

Cited by 12 publications

(12 citation statements)

References 34 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We demonstrate the application of our proposed method by analyzing a breast cancer dataset from , which was also studied by and Molstad and Rothman (2016). The dataset is available in the R package PMA, and consists of measured gene expression profiles (GEPs) and DNA copy-number variations (CVNs) for n = 89 subjects.…”

Section: Real Data Analysismentioning

confidence: 99%

Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

He¹,

Jiang²,

Wen³

et al. 2021

STAT SINICA

View full text Add to dashboard Cite

Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the structure of the regression coefficients matrix, and the likelihood ratio test (LRT) is one of the most popular approaches in practice.Despite its popularity, it is known that the classical χ 2 approximations for LRTs often fail in high-dimensional settings, where the dimensions of responses and predictors (m, p) are allowed to grow with the sample size n. Though various corrected LRTs and other test statistics have been proposed in the literature, the important question of when the classic LRT starts to fail is less studied; an answer to this would provide insights for practitioners, especially when analyzing data with m/n and p/n small but not negligible. Moreover, the power performance of the LRT in high-dimensional data analysis remains underexplored. To address these issues, the first part of this work gives the asymptotic boundary where the classical LRT fails and develops the corrected limiting distribution of the LRT for a general asymptotic regime. The second part of this work further studies the test power of the LRT in the high-dimensional settings. The result not only advances the current understanding arXiv:1812.06894v2 [math.ST] 3 Oct 2019 of asymptotic behavior of the LRT under alternative hypothesis, but also motivates the development of a power-enhanced LRT. The third part of this work considers the settingwith p > n, where the LRT is not well-defined. We propose a two-step testing procedure by first performing dimension reduction and then applying the proposed LRT. Theoretical properties are developed to ensure the validity of the proposed method. Numerical studies are also presented to demonstrate its good performance.

show abstract

Section: Real Data Analysismentioning

confidence: 99%

Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

He¹,

Jiang²,

Wen³

et al. 2021

STAT SINICA

View full text Add to dashboard Cite

show abstract

“…The breast cancer dataset was detailed described by Chin et al (2006) and analyzed by Witten et al (2009), Chen et al (2013) and Molstad and Rothman (2016). The dataset is publicly available in the R package PMA (Witten et al, 2009 The means of the prediction errors with their standard errors are presented in Table 9.…”

Section: Genomic Data Examplementioning

confidence: 99%

On Sure Screening with Multiple Responses

Zou¹,

He²,

Zhou³

2021

STAT SINICA

View full text Add to dashboard Cite

Multivariate responses are commonly encountered in many applications with high dimensional input variables. Feature screening has been shown to be a very useful data analysis tool for high dimensional data. Since the sure independence screening paper by Fan and Lv (2008), many variable screening methods have been proposed and studied in the literature. Yet, the majority of the existing screening methods handle the classical univariate response data case and do not apply naturally to the multiple responses datasets. In this paper, we systematically study variable screening methods for multi-response data. First, we consider extensions of several popular screening methods to deal with multiple responses. Each of these methods has its own clear drawbacks. We then propose a new model-free screening method named multi-response rank canonical correlation screening (mRCC). It not only takes into account the dependence structure among the multivariate responses but also preserves nice properties of the rank correlation such as robustness and invariance under monotonic transformation. The sure screening property of mRCC is established under weak regular

show abstract

“…There also exist methods with two steps: they first estimate 1 *   and then plug this estimate into a penalized normal negative log-likelihood to estimate *  (Perrot-Dockès et al, 2018). There are also methods that add an assumption that the predictor and response are () pq  -variate normal and develop estimators based on the inverse regression (Molstad and Rothman, 2016) or based on estimating the joint covariance matrix (Lee and Liu, 2012).…”

Section: Introductionmentioning

confidence: 99%

An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

Molstad

Weng

Doss

et al. 2021

Journal of Computational and Graphical Statistics

Self Cite

View full text Add to dashboard Cite

We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations between entries in the multivariate error random vector are proportional to the cosines of the angles between their corresponding regression coefficient matrix columns, so as the angle between two regression coefficient matrix columns decreases, the correlation between the corresponding errors increases. We highlight two models under which this parameterization arises: a latent variable reduced-rank regression model and the errors-in-variables regression model. We propose a novel non-convex weighted residual sum of squares criterion which exploits this parameterization and admits a new class of penalized estimators. The optimization is solved with an accelerated proximal gradient descent algorithm. Our method is used to study the association between microRNA expression and cancer drug activity measured on the NCI-60 cell lines. An R package implementing our method, MCMVR, is available online.

show abstract

Indirect multivariate response linear regression

Cited by 12 publications

References 34 publications

Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension

On Sure Screening with Multiple Responses

An Explicit Mean-Covariance Parameterization for Multivariate Response Linear Regression

Contact Info

Product

Resources

About