A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables

Oda, Ryoya; Yanagihara, Hirokazu

doi:10.1214/20-ejs1701

Cited by 10 publications

(2 citation statements)

References 23 publications

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“…There are different methods to choose the covariates that will be included in B, but these are not a primary focus of this work. For more information about covariate selection methods see [24] and [32] and references therein. In Section 5 below we work with a certain selection algorithm defined there.…”

Section: In the Second Scenario The Variance Reduction Of T B Is Appr...mentioning

confidence: 99%

Improved estimators for semi-supervised high-dimensional regression model

Ilan

Azriel

Goldberg

2022

Electron. J. Statist.

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We study a high-dimensional linear regression model in a semisupervised setting, where for many observations only the vector of covariates X is given with no responses Y . We do not make any sparsity assumptions on the vector of coefficients, nor do we assume normality of the covariates. We aim at estimating the signal level, i.e., the amount of variation in the response that can be explained by the set of covariates. We propose an estimator, which is unbiased, consistent, and asymptotically normal. This estimator can be improved by adding zero-estimators arising from the unlabeled data. Adding zero-estimators does not affect the bias and potentially can reduce the variance. We further present an algorithm based on our approach that improves any given signal level estimator. Our theoretical results are demonstrated in a simulation study.

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Section: In the Second Scenario The Variance Reduction Of T B Is Appr...mentioning

confidence: 99%

Improved estimators for semi-supervised high-dimensional regression model

Ilan

Azriel

Goldberg

2022

Electron. J. Statist.

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show abstract

“…See e.g., Zambom and Kim (2018) and Oda et al (2020) and references therein. Different covariate selection methods have different pros and cons and there is no simple answer for the question of which method to use.…”

Section: Covariate Selectionmentioning

confidence: 99%

Improved Estimators for Semi-supervised High-dimensional Regression Model

Ilan¹,

Azriel²,

Goldberg³

2021

Preprint

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We study a linear high-dimensional regression model in a semi-supervised setting, where for many observations only the vector of covariates X is given with no response Y . We do not make any sparsity assumptions on the vector of coefficients, and aim at estimating Var(Y |X). We propose an estimator, which is unbiased, consistent, and asymptotically normal. This estimator can be improved by adding zero-estimators arising from the unlabelled data. Adding zero-estimators does not affect the bias and potentially can reduce variance. In order to achieve optimal improvement, many zero-estimators should be used, but this raises the problem of estimating many parameters. Therefore, we introduce covariate selection algorithms that identify which zero-estimators should be used in order to improve the above estimator. We further illustrate our approach for other estimators, and present an algorithm that improves estimation for any given variance estimator. Our theoretical results are demonstrated in a simulation study.

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A Consistent Likelihood-Based Variable Selection Method in Normal Multivariate Linear Regression

Oda

Yanagihara

2021

Intelligent Decision Technologies

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A fast and consistent variable selection method for high-dimensional multivariate linear regression with a large number of explanatory variables

Cited by 10 publications

References 23 publications

Improved estimators for semi-supervised high-dimensional regression model

Improved estimators for semi-supervised high-dimensional regression model

Improved Estimators for Semi-supervised High-dimensional Regression Model

A Consistent Likelihood-Based Variable Selection Method in Normal Multivariate Linear Regression

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