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Bootstrap Resampling

Statistical and Numerical Computing

  1. Philip M. Dixon

Published Online: 15 SEP 2006

DOI: 10.1002/9780470057339.vab028

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Dixon, P. M. 2006. Bootstrap Resampling. Encyclopedia of Environmetrics. 1.

Author Information

  1. Iowa State University, IA, USA

Publication History

  1. Published Online: 15 SEP 2006
Table 1. Methods for Estimating Endpoints of Bootstrap α-Level Confidence Intervals. equation image is the Observed Estimate, equation image is the Bootstrap CDF, equation image is the Studentized Bootstrap CDF, Φ(x) is the Normal CDF, equation image, a is the Acceleration Constant, and zα is the α-Percentile of a Standard Normal Distribution
Methodα-level endpointRange preserving?
Percentileequation imageYes
Acceleratedequation imageYes
ABCequation imageNo
Basicequation imageNo
Studentizedequation imageNo
Table 2. Parameter Estimates, Bootstrap Estimate of Bias, and Bootstrap Estimate of the SE for Four Quantities Describing the Relationship between Urine Creatinine and Magnesium Concentrations
StatisticEstimateBiasSE
Correlation0.4090.005 430.0752
Slope, Kapfenberg232.92.9338.5
Slope, Knittelfeld105.2−1.2813.7
Ratio of slopes2.2150.0560.508
Table 3. Endpoints of 95% Confidence Intervals for Four Quantities Describing the Relationship between Urine Creatinine and Magnesium Concentrations. Confidence Intervals are Computed Using the Percentile, Basic and BCa Methods. The Studentized Bootstrap is Included when it Could be Calculated Easily
StatisticBootstrap confidence interval method95% confidence interval
CorrelationPercentile(0.252, 0.553)
Basic(0.265, 0.566)
BCa(0.227, 0.525)
ABC(0.252, 0.542)
Slope, β1 KapfenbergPercentile(166.0, 312.1)
Basic(153.8, 300.0)
BCa(162.8, 308.6)
Studentized(143.8, 304.1)
Slope, β2 KnittelfeldPercentile(73.9, 128.9)
Basic(81.4, 136.4)
BCa(75.8, 130.9)
Studentized(79.9, 134.7)
Ratio of slopesPercentile(1.44, 3.44)
Basic(0.99, 2.99)
BCa(1.48, 3.55)
Studentized(1.47, 3.35)