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- W2282569749 abstract "Let X = (X1; : : : ; Xn) be a random sample and be a scalar parameter. A conventional level two-sided bootstrap interval I for typically has coverage error of order O(n ). A general application of the iterated bootstrap involves (i) embedding I in a broad class of bootstrap intervals I(t) calibrated by t, (ii) choosing t to satisfy P ( 2 I (t) j X ) = , where I (t) is the version of I(t) computed on a bootstrap resample drawn from X , and (iii) de ning the iterated bootstrap interval to be J = I(t). [3] shows that the coverage error of J is reduced to O(n ). In practice, Monte Carlo approximation to J requires the drawing of B rst-level resamples to approximate I(t) and the probability in step (ii), and the drawing of C second-level bootstrap resamples from each rst-level resample to calculate I (t). The intrinsic sampling error of the iterated bootstrap is thus overlaid with a certain Monte Carlo error induced by nite simulation. This article focuses on three di erent algorithms for approximating J , studies the interplay of sampling and Monte Carlo errors, and makes recommendation on choices of B and C for the algorithms. We assume, as in [1], validity of Edgeworth expansions in order to establish asymptotic expansions for the coverage probabilities." @default.
- W2282569749 created "2016-06-24" @default.
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- W2282569749 date "1999-01-01" @default.
- W2282569749 modified "2023-09-27" @default.
- W2282569749 title "Monte Carlo vs sampling error in construction of iterated bootstrap confidence intervals" @default.
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- W2282569749 hasPublicationYear "1999" @default.
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