  We provide adaptive confidence intervals on a parameter of interest in the
presence of nuisance parameters when some of the nuisance parameters have known
signs. The confidence intervals are adaptive in the sense that they tend to be
short at and near the points where the nuisance parameters are equal to zero.
We focus our results primarily on the practical problem of inference on a
coefficient of interest in the linear regression model when it is unclear
whether or not it is necessary to include a subset of control variables whose
partial effects on the dependent variable have known directions (signs). Our
confidence intervals are trivial to compute and can provide significant length
reductions relative to standard confidence intervals in cases for which the
control variables do not have large effects. At the same time, they entail
minimal length increases at any parameter values. We prove that our confidence
intervals are asymptotically valid uniformly over the parameter space and
illustrate their length properties in an empirical application to a factorial
design field experiment and a Monte Carlo study calibrated to the empirical
application.
