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

Arbeitspapier

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 »0, a parameter in front of the regressor of interest, such as the treatment variable or a policy variable. These methods allow to estimate »0 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.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: cemmap working paper ; No. CWP67/13

Klassifikation und Themen

• Klassifikation: Wirtschaft
• Thema: uniformly valid inference ; instruments ; double selection ; Neymanization ; optimality ; sparsity ; model selection

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Belloni, Alexandre ; Chernozhukov, Victor ; Wei, Ying
• Ereignis: Veröffentlichung
• (wer): Centre for Microdata Methods and Practice (cemmap)
• (wo): London
• (wann): 2013

Weitere Informationen

• DOI: doi:10.1920/wp.cem.2013.6713
• Handle: http://hdl.handle.net/10419/97416
• Letzte Aktualisierung: 10.03.2025, 11:43 MEZ