Bootstrap—An exploration

We review a few unusual aspects of Bootstrap and some of the recent theoretical as well as methodological advances. We discuss the handling of non-linearity by Bootstrap through a numerical example in Section  2. Application to the estimation of high-dimensional inverse covariance matrix is presented in Section  3 with emphasis on the Augmented Bootstrap and a Bayesian version of it. Another high dimensional example, namely, Random Forest and its offshoot random survival forest (Ishwaran et al. (2008)  [32]) are discussed in Section  4. Bootstrap for massive data, introduced by Kleiner et al. (2011) [35], is discussed in Section  4. In Section  5, we discuss some aspects of Bootstrap in the context of hypothesis testing in high-dimension.