The next RSS Journal webinar will be held on 2nd April at 4pm (UK time); 11am (EDT or UTC-4h)

Paper: ‘Confidence intervals for low dimensional parameters in high dimensional linear models’
by Cun-Hui Zhang and Stephanie S Zhang.

The paper was published in JRSS Series B (Vol 76:1) in January 2014. It is an open access paper available from the Wiley Online Library.

Abstract
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.

Presenter
Cun-Hui Zhang will present and discuss his paper, which is co-authored by Stephani S Zhang.

Chair
Yi Yu, University of Bristol

Discussants
Andrea Montenari, Stanford University and Sara van de Geer, ETH Zurich

An open discussion led by our discussants will follow the presentation by Cun-Hui Zhang in which everyone is encouraged to take part. You can ask the author a question over the phone or type a message if you prefer using the web based teleconference system (Skype).

Questions can also be emailed in advance and further information requested from [email protected].

Full event details including slides (when available) can be found on our website

Journal webinars are free, open to everyone and simple to join.

Those unable to listen in live will be able to listen to the podcast and view slides from the presentation afterwards on YouTube, accessible from the main RSS website.