2011

Confidence Intervals for Low-Dimensional Parameters in High-Dimensional Linear Models

Zhang, Cun-Hui, Zhang, Stephanie S.

Understand

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 broad context.
The theoretical results presented here 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 far exceed the sample size.

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