The conventional Edgeworth expansion view of bootstrap confidence intervals suggests that for the bootstrap to exceed the accuracy of the normal approximation one must bootstrap asymptotically pivotal statistics. This paper questions the basic premise of the asymptotic theory used to rationalize the higher-order accuracy of bootstrap intervals for asymptotically pivotal statistics. In finite samples, these statistics often are not even approximately pivotal. As a result, Edgeworth expansion arguments for pivotal statistics do not apply, and the only way to compare the accuracy of alternative intervals is by simulation. The paper documents that percentile-t intervals based on asymptotic pivots tend to behave erratically in small samples and may be much less accurate than bootstrap intervals based on nonpivotal statistics. It is also shown that bootstrap intervals can be very accurate in the absence of asymptotic refinements, and that there are huge differences in coverage accuracy among asymptotically equivalent intervals that cannot be explained by Edgeworth expansion arguments.
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Paper provided by Michigan - Center for Research on Economic & Social Theory in its series Papers with number
98-04.
Length: 34 pages Date of creation: 1998 Date of revision: Handle: RePEc:fth:michet:98-04
Contact details of provider: Postal: UNIVERSITY OF MICHIGAN, DEPARTMENT OF ECONOMICS CENTER FOR RESEARCH ON ECONOMIC AND SOCIAL THEORY, ANN ARBOR MICHIGAN U.S.A.
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Find related papers by JEL classification: C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
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