This paper studies the problem of specification testing in partially identified models defined by a finite number of moment equalities and inequalities (i.e., (in)equalities). Under the null hypothesis, there is at least one parameter value that simultaneously satisfies all of the moment...

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...</<>

This paper introduces a new hypothesis test for the null hypothesis H0 : f(Ø) = Y0, where f(.) is a known function, Y0 is a known constant, and Ø is a parameter that is partially identified by a moment (in)equality model. The main application of our test is sub-vector inference in moment...

In the microsimulation literature, it is still uncommon to test the statistical significance of results. In this paper we argue that this situation is both undesirable and unnecessary. Provided the parameters used in the microsimulation are exogenous, as is often the case in static...

This paper studies the problem of specification testing in partially identified models defined by a finite number of moment equalities and inequalities (i.e. (in)equalities). Under the null hypothesis, there is at least one parameter value that simultaneously satisfies all of the moment...

This paper introduces a bootstrap-based inference method for functions of the parameter vector in a moment (in)equality model. As a special case, our method yields marginal confidence sets for individual coordinates of this parameter vector. Our inference method controls asymptotic size...