Although it is common to refer to “the bootstrap,” there are actually a great many different bootstrap methods that can be used in econometrics. We emphasize the use of bootstrap methods for inference, particularly hypothesis testing, and we also discuss bootstrap confidence intervals. There are important cases in which bootstrap inference tends to be more accurate than asymptotic inference. Ho...

Purdue University and Texas A&M University Consider M-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and a nuisance function parameter. We show that, under general conditions, the bootstrap is asymptotically consistent in estimating the distribution of the Mestimate of Euclidean parameter; that is, the bootstrap distribution asymptotically imitat...

The fundamental bootstrap assumption is that the bootstrap approximates reality; that the sampling distribution of a statistic under the empirical distribution F̂ approximates the sampling distribution under the true (unknown) distribution. A natural way to test this is to investigate how the bootstrap distribution varies when F̂ is replaced by other distributions. Iterated bootstrapping, jackkni...

results slow and fast-growing groups of the mycobacterium strains were clearly differentiated based on the constructed tree of 56 common mycobacterium isolates. each species with a unique title in the tree was identified; in total, 13 nods with a bootstrap value of over 50% were supported. among the slow-growing group was mycobacterium kansasii, with m. tuberculosis in a cluster with a bootstra...

I propose a nonparametric iid bootstrap that achieves asymptotic refinements for t tests and confidence intervals based on the generalized method of moments (GMM) estimators even when the model is misspecified. In addition, my bootstrap does not require recentering the bootstrap moment function, which has been considered as a critical procedure for bootstrapping GMM. The elimination of the rece...

We study the bootstrap estimator of the sampling distribution of a given statistic in some nonregular cases where the given statistic is nonsmooth or not-so-smooth. It is found that the ordinary bootstrap, based on a bootstrap sample of the same size as the original data set, produces an inconsistent bootstrap estimator. On the other hand, when we draw a bootstrap sample of a smaller size with ...

We propose a generalization of the wild bootstrap of Wu (1986) and Liu (1988) based upon perturbing the scores of M-estimators. This “score bootstrap” procedure avoids recomputing the estimator in each bootstrap iteration, making it substantially less costly to compute than the conventional nonparametric bootstrap, particularly in complex nonlinear models. Despite this computational advantage, ...

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets which are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently Kleiner, Talwalkar, Sarkar, and Jordan (2014) proposed a method called BL...

The true probability distribution of a test statistic is rarely known. Generally, its asymptotic law is used as approximation of the true law. If the sample size is not large enough, the asymptotic behavior of that statistic could lead to a poor approximation of the true one. Using bootstrap methods, under some regularity conditions, it is possible to obtain a more accurate approximation of the...