  We propose a method to remedy finite sample coverage problems and improve
upon the efficiency of commonly employed procedures for the construction of
nonparametric confidence intervals in regression kink designs. The proposed
interval is centered at the half-length optimal, numerically obtained linear
minimax estimator over distributions with Lipschitz constrained conditional
mean function. Its construction ensures excellent finite sample coverage and
length properties which are demonstrated in a simulation study and an empirical
illustration. Given the Lipschitz constant that governs how much curvature one
plausibly allows for, the procedure is fully data driven, computationally
inexpensive, incorporates shape constraints and is valid irrespective of the
distribution of the assignment variable.
