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Model selection has an important impact on subsequent inference. Ignoring the model selection step leads to invalid inference. We discuss some intricate aspects of data-driven model selection that do… (More)

We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges’ estimator. The… (More)

- Benedikt M. Pötscher, Hannes Leeb
- J. Multivariate Analysis
- 2007

We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the… (More)

We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure… (More)

- Hannes Leeb, Benedikt M. Poetscher
- 2000

In Poetscher [Econometric Theory (1991), 7, pp 163 - 185] the asymptotic distribution of a post-model-selection estimator, both unconditional and conditional on selecting a correct model, has been… (More)

- Paul Kabaila, Hannes Leeb
- 2006

We give a large-sample analysis of the minimal coverage probability of the usual confidence intervals for regression parameters when the underlying model is chosen by a “conservative” (or… (More)

- Hannes Leeb
- 2006

We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample… (More)

We compare several confidence intervals after model selection in the setting recently studied by Berk et al. (2013), where the goal is to cover not the true parameter but a certain non-standard… (More)

One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant.… (More)

- Hannes Leeb
- 2009

We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the… (More)