Confidence Intervals for Low Dimensional Parameters in High Dimensional Linear Models

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ID: 298922
2013
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Ranked #3 of 145 articles by views in Journal of the Royal Statistical Society Series B (Statistical Methodology)

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Abstract
Summary The purpose of this paper is to propose methodologies for statistical inference of low dimensional parameters with high dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of several of them in a linear regression model, although our ideas are applicable in a much broader context. The theoretical results that are presented provide sufficient conditions for the asymptotic normality of the proposed estimators along with a consistent estimator for their finite dimensional covariance matrices. These sufficient conditions allow the number of variables to exceed the sample size and the presence of many small non-zero coefficients. Our methods and theory apply to interval estimation of a preconceived regression coefficient or contrast as well as simultaneous interval estimation of many regression coefficients. Moreover, the method proposed turns the regression data into an approximate Gaussian sequence of point estimators of individual regression coefficients, which can be used to select variables after proper thresholding. The simulation results that are presented demonstrate the accuracy of the coverage probability of the confidence intervals proposed as well as other desirable properties, strongly supporting the theoretical results.
Reference Key
openalex_W2069119359 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Cun‐Hui Zhang, Stephanie S. Zhang
Journal Journal of the Royal Statistical Society Series B (Statistical Methodology)
Year 2013
DOI
10.1111/rssb.12026
URL
https://doi.org/10.1111/rssb.12026
Keywords Keywords not found

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