"If there was ever an idea in statistics which evokes the reaction, 'Why the hell didn’t I think of that', it has to be the bootstrap." (James R Thompson, [Interface Proceedings] 1997)
"This computationally intensive operation [bootstrapping] is not one calculated to endear a user to a database administrator." (Leland Wilkinson, "The Grammar of Graphics", 1999)
"The estimate of the standard error (SE) is more sensitive to the Normality assumption than the estimate of the coefficients. There are two options available which do not require this assumption; these are the bootstrap and the robust standard error." (Michael J Campbell, "Statistics at Square Two: Understanding modern statistical applications in medicine" 2nd Ed., 2006)
"Not all data sets lend themselves to data splitting. The data set may be too small to split and/or the fitted model may be a local smoother. In the first case, there is too little data upon which to build a model if the data is split; and in the second case, it is not expected the model for any part of the data to directly interpolate/extrapolate to any other part of the model. For these cases, a different approach to cross-validation is possible, something similar to bootstrapping." (DeWayne R Derryberry, "Basic Data Analysis for Time Series with R" 1st Ed, 2014)
"An obvious question is: do bootstrapped confidence intervals satisfy the frequentist coverage property? If your sample is fairly representative of the population, then the answer is a qualified yes. That is, the bootstrapping procedure yields nominal X% intervals that cover the true value 'approximately' X% of the time. Moreover, as the size of the original sample gets bigger, the quality of the approximation gets better. Alas, it is necessary to appeal to some very advanced probability theory to put both of these claims on firm footing." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)
"At the core of the resampling approach to statistical inference lies a simple idea. Most of the time, we can’t feasibly take repeated samples of size n from the population, to see how our estimate changes from one sample to the next. But we can repeatedly take samples of size n from the sample itself, and apply our estimator afresh to each notional sample. The idea is that the variability of the estimates across all these samples can be used to approximate our estimator’s true sampling distribution. This process—pretending that our sample is the whole population, and taking repeated samples of size n with replacement from our original sample of size n - is called bootstrap resampling, or just bootstrapping" (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)
"Resampling won’t yield the true sampling distribution of an estimator, but it is often good enough for approximating the standard error (which you’ll remember is just the standard deviation of the sampling distribution). We use the term bootstrapped standard error for the standard deviation of the bootstrapped sampling distribution. The bootstrapped standard error is an estimate of the true standard error." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)
"Bootstrapping provides an intuitive, computer-intensive way of assessing the uncertainty in our estimates, without making strong assumptions and without using probability theory. But the technique is not feasible when it comes to, say, working out the margins of error on unemployment surveys of 100,000 people. Although bootstrapping is a simple, brilliant and extraordinarily effective idea, it is just too clumsy to bootstrap such large quantities of data, especially when a convenient theory exists that can generate formulae for the width of uncertainty intervals." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)
"But [bootstrap-based] simulations are clumsy and time-consuming, especially with large data sets, and in more complex circumstances it is not straightforward to work out what should be simulated. In contrast, formulae derived from probability theory provide both insight and convenience, and always lead to the same answer since they don’t depend on a particular simulation. But the flip side is that this theory relies on assumptions, and we should be careful not to be deluded by the impressive algebra into accepting unjustified conclusions." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)
"What recourse do we have if our groups do not have homogeneous variances? If we stick to parametric statistics, when we use a t-test, there is a correction that is performed for groups whose variances are not the same. If we use an ANOVA there is no such correction, but we could choose not to compare groups that have non-homogeneous variances or combine certain groups to achieve a better effect. Again, the main effect of not having homogeneous variances is that, although group differences may actually exist, we might not be able to find them. Thus, if you perform a statistical test and find that the group differences you thought would be there are not found, you might consider that this result is due to non-homogeneous variances.Another possibility to avoid problems with non-homogeneous groups is to use robust statistical procedures, such as bootstrapping and means trimming. These robust methods deal with problems due to both violations of normal distributions and homogeneity of variances in a manner that is objective and more robust to violations than parametric statistics." (Jenifer Larson-Hall, "A Guide to Doing Statistics in Second Language Research Using SPSS and R" 2nd Ed., 2016)
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