Model specification and selection are recurring themes in econometric analysis. Both topics become considerably more complicated in the case of large-dimensional data sets where the set of specification possibilities can become quite large. In the context of linear regression models, penalised...

The paper proposes a new algorithm for finding the confidence set of a collection of forecasts or prediction models. Existing numerical implementations for finding the confidence set use an elimination approach where one starts with the full collection of models and successively eliminates the...

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...

We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse least absolute deviation/median regression model. The setting is one where the number of regressors p could be large in comparison to the sample size n, but only s << n of them are needed to accurately describe the regression function. Our new methods are based on the instrumental median regression estimator that assembles the optimal estimating equation from the output of the post l1-penalized median regression and post l1-penalized least squares in an auxiliary equation. The estimating equation is immunized against non-regular estimation of nuisance part of the median regression function, in the sense of Neyman. We establish that in a homoscedastic regression model, the instrumental median regression estimator of a single regression coefficient is asymptotically root-n normal uniformly with respect to the underlying sparse model. The resulting confidence regions are valid uniformly with respect to the underlying model. We illustrate the value of uniformity with Monte-Carlo experiments which demonstrate that standard/naive post-selection inference breaks down over large parts of the parameter space, and the proposed method does not. We then generalize our method to the case where p1 > n regression coefficients...</<>

We explore the benefits of forecast combinations based on forecast- encompassing tests compared to simple averages and to Bates-Granger combinations. We also consider a new combination method that fuses test-based and Bates-Granger weighting. For a realistic simulation design, we generate...