Discussion Bootstrapping (statistics)

1 discussion

1.1 advantages
1.2 disadvantages
1.3 recommendations

discussion

advantages

a great advantage of bootstrap simplicity. straightforward way derive estimates of standard errors , confidence intervals complex estimators of complex parameters of distribution, such percentile points, proportions, odds ratio, , correlation coefficients. bootstrap appropriate way control , check stability of results. although problems impossible know true confidence interval, bootstrap asymptotically more accurate standard intervals obtained using sample variance , assumptions of normality.

disadvantages

although bootstrapping (under conditions) asymptotically consistent, not provide general finite-sample guarantees. apparent simplicity may conceal fact important assumptions being made when undertaking bootstrap analysis (e.g. independence of samples) these more formally stated in other approaches.

recommendations

the number of bootstrap samples recommended in literature has increased available computing power has increased. if results may have substantial real-world consequences, 1 should use many samples reasonable, given available computing power , time. increasing number of samples cannot increase amount of information in original data; can reduce effects of random sampling errors can arise bootstrap procedure itself.

adèr et al. recommend bootstrap procedure following situations:

when theoretical distribution of statistic of interest complicated or unknown. since bootstrapping procedure distribution-independent provides indirect method assess properties of distribution underlying sample , parameters of interest derived distribution.






when sample size insufficient straightforward statistical inference. if underlying distribution well-known, bootstrapping provides way account distortions caused specific sample may not representative of population.






when power calculations have performed, , small pilot sample available. power , sample size calculations heavily dependent on standard deviation of statistic of interest. if estimate used incorrect, required sample size wrong. 1 method impression of variation of statistic use small pilot sample , perform bootstrapping on impression of variance.

however, athreya has shown if 1 performs naive bootstrap on sample mean when underlying population lacks finite variance (for example, power law distribution), bootstrap distribution not converge same limit sample mean. result, confidence intervals on basis of monte carlo simulation of bootstrap misleading. athreya states unless 1 reasonably sure underlying distribution not heavy tailed, 1 should hesitate use naive bootstrap .