Theoretical Comparison of Bootstrap Confidence Intervals

By Peter Hall. 1988

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Citations in the corpus

Trend analysis of climate time series: A review of methods (2019, background): “Efron and Tibshirani (1986) and Hall (1988) pursued the construction of confidence intervals from bootstrap replications.”
Advantages of Monte Carlo Confidence Intervals for Indirect Effects (2012, background): “176; Efron & Tibshirani, 1993 ; Hall, 1989 ), meaning that coverage rates approach the nominal value very quickly as N increases.”
Estimation of the stress-strength reliability for the generalized logistic distribution (2013, methodology): “In this subsection, we propose to use two confidence intervals based on the parametric bootstrap methods: (i) the percentile bootstrap method (we call it Boot-p) based on the idea of Efron [11], and (ii) the bootstrap-t method (we refer to it as Boot-t) based on the idea of Hall [16].”
Exact inference for progressively Type-I censored exponential failure data (2011, methodology): “In this subsection, we discuss the construction of the CI for θ using a parametric bootstrap method, v iz ., the bias-corrected and accelerated (BCa) percentile bootstrap method; see Efron (1987), Hall (1988) , and Efron and Tibshirani (1993) for pertinent details.”
Analysis of Type-II progressively hybrid censored data (2006, methodology): “[13] Hall, P. (1988), " Theoretical comparison of bootstrap confidence intervals " , Annals of Statistics, vol. 16, 927 -953.”
LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II (2003, background): “If one assumes that Q has a nonzero absolutely continuous component with respect to the volume measure on M , then from some results of Bhattacharya and Ghosh [6], Babu and Singh [1], Beran [2] and Hall [24, 25], one derives bootstrap-based confidence regions for µE(Q) with coverage error Op(n −2) (”
Estimating Pearson's Correlation Coefficient with Bootstrap Confidence Interval from Serially Dependent Time Series (2003, background): “|( j ))/n. Hall (1988) proved that BCa confidence intervals have advantageous second-order accuracy: letrxy(α) be the single endpoint of confidence interval forρxy with nominal one-sided coverageα, then Prob[ρxy ≤ rxy(α)] = α + C with the coverage error, C, being of order (1/n).”
Comparison of Different Estimators of P [Y < X] for a Scaled Burr Type X Distribution (2005, methodology): “The following two confidence intervals mainly for small sample sizes, which might be computationally very demanding for large sample, are proposed, namely; (i) percentile bootstrap method (we call it from now on as Boot-p) based on the original idea of Efron [7] and (ii) bootstrap-t method (we refer”
Analysis of Incomplete Data in Presence of Competing Risks (2000, methodology): “ Hall (1988) showed that the bootstrap-t condence interval is better than the percentile bootstrap condence intervals from an asymptotic point of view, although the nite sample properties are not yet known.”