centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Honest confidence regions for a regression parameter in logistic regression with a large number of controls

Authors: Alexandre Belloni , Victor Chernozhukov and Ying Wei
Date: 30 December 2013
Type: cemmap Working Paper, CWP67/13
DOI: 10.1920/wp.cem.2013.6713


This paper considers inference in logistic regression models with high dimensional data. We propose new methods for estimating and constructing confidence regions for a regression parameter of primary interest α0 a parameter in front of the regressor of interest, such as the treatment variable or policy variable. These methods allow to estimate α0 at the root-n rate when the total number p of other regressors, called controls, exceed the sample size n, using the sparsity assumptions. The sparsity assumption means that only s unknown controls are needed to accurately approximate the nuisance part of the regression function, where s is smaller than n. Importantly, the estimators and these resulting confidence regions are 'honest' in the formal sense that their properties hold uniformly over s-sparse models. Moreover, these procedures do not rely on traditional 'consistent model selection' arguments for their validity; in fact, they are robust with respect to 'moderate' model selection mistakes in variable selection steps. Moreover, the estimators are semi-parametrically efficient in the sense of attaining the semi-parametric efficiency bounds for the class of models in this paper. Download full version

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us