On the relative accuracy of certain bootstrap procedures. (English) Zbl 0941.62053
Summary: We show the second-order relative accuracy, on bounded sets, of the Studentized bootstrap, exponentially tilted bootstrap and nonparametric likelihood tilted bootstrap, for means and smooth functions of means. We also consider the relative errors for larger deviations. Our method exploits certain connections between Edgeworth and saddlepoint approximations to simplify the computations.
MSC:
| 62G09 | Nonparametric statistical resampling methods |
| 62G20 | Asymptotic properties of nonparametric inference |
| 62G10 | Nonparametric hypothesis testing |
Keywords:
bootstrap approximation; Edgeworth expansions; empirical likelihood; exponential tilting; Studentizing; saddlepoint approximationsReferences:
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