We develop uniformly valid confidence regions for a regression coefficient in a high-dimensional sparse LAD (least absolute deviation or 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...

Using the Reinhart-Rogoff dataset, we find a debt threshold not around 90 percent but around 30 percent above which the median real GDP growth falls abruptly. Our work is the first to formally test for threshold effects in the relationship between public debt and median real GDP growth. The null...

We consider estimation of a linear or nonparametric additive model in which a few coefficients or additive components are "large" and may be objects of substantive interest, whereas others are "small" but not necessarily zero. The number of small coefficients or additive components may exceed...