Confidence intervals in regression centred on the SCAD estimator

TL;DR

This paper investigates the construction of confidence intervals centered on the SCAD estimator in linear regression, examining whether these intervals can retain desirable properties similar to the estimator itself.

Contribution

It extends the analysis of the SCAD estimator by exploring the properties of confidence intervals centered on it in the context of linear regression.

Findings

Interval estimators can exhibit properties similar to the SCAD estimator.

Analysis is conducted under orthonormal design matrix assumptions.

The paper provides insights into the potential of SCAD-centered confidence intervals.

Abstract

Consider a linear regression model. Fan and Li (2001) describe the smoothly clipped absolute deviation (SCAD) point estimator of the regression parameter vector. To gain insight into the properties of this estimator, they consider an orthonormal design matrix and focus on the estimation of a specified component of this vector. They show that the SCAD point estimator has three attractive properties. We answer the question: To what extent can an interval estimator, centred on the SCAD estimator, have similar attractive properties?