## Statistical Science

- Statist. Sci.
- Volume 30, Number 2 (2015), 216-227.

### On Various Confidence Intervals Post-Model-Selection

Hannes Leeb, Benedikt M. Pötscher, and Karl Ewald

#### Abstract

We compare several confidence intervals after model selection in the setting recently studied by Berk et al. [
*Ann. Statist.*
**41** (2013) 802–837], where the goal is to cover not the true parameter but a certain nonstandard quantity of interest that depends on the selected model. In particular, we compare the PoSI-intervals that are proposed in that reference with the “naive” confidence interval, which is constructed as if the selected model were correct and fixed a priori (thus ignoring the presence of model selection). Overall, we find that the actual coverage probabilities of all these intervals deviate only moderately from the desired nominal coverage probability. This finding is in stark contrast to several papers in the existing literature, where the goal is to cover the true parameter.

#### Article information

**Source**

Statist. Sci., Volume 30, Number 2 (2015), 216-227.

**Dates**

First available in Project Euclid: 3 June 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.ss/1433341479

**Digital Object Identifier**

doi:10.1214/14-STS507

**Mathematical Reviews number (MathSciNet)**

MR3353104

**Zentralblatt MATH identifier**

1332.62154

**Keywords**

Confidence intervals model selection nonstandard coverage target AIC BIC Lasso

#### Citation

Leeb, Hannes; Pötscher, Benedikt M.; Ewald, Karl. On Various Confidence Intervals Post-Model-Selection. Statist. Sci. 30 (2015), no. 2, 216--227. doi:10.1214/14-STS507. https://projecteuclid.org/euclid.ss/1433341479