Nonparametric bootstrapping

boot

Confidence interval for $$\mu$$

Using package boot

Function to calculate the mean and uncorrected variance (=plug-in estimator for the population variance) of a given replication.

ORDINARY NONPARAMETRIC BOOTSTRAP

Call:
boot(data = DV, statistic = getM, R = nR)

Bootstrap Statistics :
original      bias    std. error
t1* 99.657182 0.068458482   2.6470886
t2*  7.080822 0.001496239   0.7552599

Various types of bootstrap confidence intervals

BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
Based on 999 bootstrap replicates

CALL :
boot.ci(boot.out = bsRes, conf = 1 - alpha, type = c("basic",
"perc", "norm", "stud", "bca"))

Intervals :
Level      Normal              Basic             Studentized
95%   ( 94.40, 104.78 )   ( 94.51, 104.70 )   ( 94.58, 104.76 )

Level     Percentile            BCa
95%   ( 94.62, 104.80 )   ( 94.39, 104.67 )
Calculations and Intervals on Original Scale

Bootstrap distribution

For the $$t$$ test statistic, compare the empirical distribution from the bootstrap replicates against the theoretical $$t_{n-1}$$ distribtion.

boot.array(boot(...), indices=TRUE) gives detailed information about the selected indices for each bootstrap replication. If the sample has $$n$$ observations, and there are $$R$$ replications, the result is an $$(R \times n)$$-matrix with one row for each replication and one column for each observation.