Bootstrap prediction intervals with asymptotic conditional validity and unconditional guarantees
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Focus on linear regression model, in this paper we introduce a bootstrap algorithm for prediction which controls the possibility of under-coverage and provide the theoretical proof on validity of this algorithm. In addition, we derive the asymptotic distribution of the difference between probability of future observation conditioning on observed data and conditional coverage probability generated by residual-based bootstrap algorithm. By applying this result, we show that residual-based bootstrap algorithm asymptotically has 50% possibility of under-coverage without modification. We perform several numerical experiments and the proposed algorithm has desired possibilities of under-coverage in those experiments with moderate sample sizes. Results mentioned in this paper can be extended to different statistical inference models, especially to dependent situations like ARMA models, Arch models and others.
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