1 Introduction In a seminal paper, Kim and Pollard (1990) studied a class of M-estimators exhibiting cube root asymptotics. These estimators not only have a non-standard rate of convergence, but also have the property that rather than being Gaussian their limiting distributions are of the Chernoff (1964) type. More precisely, the limiting distribution of 3 √$_{n}$ times their estimation error is that of the maximizer of a Gaussian process (where n denotes the sample size). In fact, in leading examples of cube root consistent estimators such as the maximum score estimator of Manski (1975), the covariance kernel of the Gaussian process characterizing the limiting distribution depends on an infinite-dimensional nuisance parameter. As a consequence, whereas it is customary to conduct inference using analytical “plug-in” covariance matrix estimators in the standard √$_{n}$$_{-normal case}$ (i.e., using a finite-dimensional nuisance parameter estimator), resampling-based distributional ap- proximations offer the most attractive approach to inference in estimation problems exhibiting cube root asymptotics. The purpose of this note is to propose an easy-to-implement bootstrap-based distributional approximation applicable in such cases. As does the standard nonparametric bootstrap, the method proposed herein employs bootstrap samples of size n from the empirical distribution function. But unlike the nonparametric bootstrap, which is inconsistent in general (e.g., Abrevaya and Huang, 2005; L´ eger and MacGibbon, 2006), our method offers a consistent distributional approximation for 3 √$_{n}$$_{-consistent estimators and therefore}$ has the advantage that it can be used to construct asymptotically valid inference procedures. Consistency is achieved by altering the shape of the criterion function defining the estimator whose distribution we seek to approximate: heuristically, the method is designed to ensure that the bootstrap version of a certain empirical process has a mean which resembles the large sample version of its population counterpart. The latter is quadratic in the problems we study and known up to the value of a certain matrix. As a consequence, the only ingredient needed to implement the proposed “reshapement” of the objective function is a consistent estimator of the unknown matrix entering the quadratic mean of the empirical process. Such estimators turn out to be generically available and easy to compute. Several alternative resampling-based distributional approximations for cube root consistent es- timators have been proposed in the literature. The best known alternative is probably subsampling 1