Publication record · 18.cifr/1979.efron.bootstrap
18.cifr/1979.efron.bootstrapWe discuss the following problem: given a random sample X = (X_1, X_2, ..., X_n) from an unknown probability distribution F, estimate the sampling distribution of some prespecified random variable R(X, F), on the basis of the observed data x. (Standard jackknife theory gives an approximate mean and variance in the case R(X,F) = theta(F_hat) - theta(F).) Our main tool is to resampling x in a simple way. The resulting 'bootstrap' distribution is shown to be consistent for a variety of applications.
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Efron's paper calls for study of bootstrap behavior on non-smooth estimators (e.g., sample median) and better understanding of confidence interval coverage accuracy. Subsequent work (BCa, bootstrap-t) addressed coverage accuracy. Efficient resampling schemes and parametric bootstrap variants address the computational cost that was a practical concern in 1979.