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Each bootstrap sample contributed one cut-point estimate, so that the standard deviation of the 200 cut-point estimates was used as the bootstrap estimator of the standard deviation (SDB) for the estimated cut-point.
The bootstrap estimator of the MISE is defined as begin{array}rcl@text{MISE}^(h)&=& mathbb{E}left[int_{-infty}^{+ infty} left[,widetilde{f}_{X}^(x;h) - widetilde{f}_{X}(x g) right]^{2},dxright], end{array} (31).
We used the non-parametric bootstrap estimator of the total number of species including the ones that were not detected [ 30, 16].
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The asymptotic expression for bootstrap estimator of MISE is begin{aligned} text{MISE}^(h)=frac{1.074}{2Nhsqrt{pi}} + frac{h^{4}}{4}int_ left(,widetilde{f}_{X}^{primeprime}(x g)right)^{2},dx +Oleft(h^{6}right), end{aligned} (D.5).
Since they need to equate the bootstrap variance of the bootstrap estimator to the Yates and Grundy's estimator (YGE) for the variance of the HTE in case of a single variable, i.e., in the linear case the YG variance estimator is required to be positive for the sample usually drawn.
Bootstrap 632 is a variant, which tries to correct the bias of the basic bootstrap estimator by performing an average with the resubstitution estimator [25]: (9).
The bootstrap estimator then performs a weighted average of the bootstrap zero and resubstitution estimators (20).
The 0.632 bootstrap estimator is obtained by averaging the errors of classifiers designed from points drawn with replacement and then taking a convex combination of this "zero bootstrap" error with the resubstitution error for the designed classifier.
The accuracy of the classifier was calculated using the 0.632 bootstrap estimator (Efron 1983).
This pathway effect can be detected significantly at α=0.05 by the percentile bootstrap and bias-corrected bootstrap CI method, as well as by PEM-UD estimated the variance via the unbiased estimator, 19 the multivariate delta estimator, 20 the bootstrap estimator.
We report the 2.5th and 97.5th percentiles from the resulting distribution of incidence for each region using a standard nonparametric bootstrap estimator that has an approximate 0.95 probability of including the true regional incidence represented by the study data [ 13].
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