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What is BOOTSTRAPPING? What does BOOTSTRAPPING mean? BOOTSTRAPPING meaning -BOOTSTRAPPING pronunciation – BOOTSTRAPPING definition – BOOTSTRAPPING explanation – How to pronounce BOOTSTRAPPING?

Source: Wikipedia.org article, adapted under https://creativecommons.org/licenses/by-sa/3.0/ license.

In statistics, bootstrapping can refer to any test or metric that relies on random sampling with replacement. Bootstrapping allows assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some other such measure) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Generally, it falls in the broader class of resampling methods.

Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples with replacement, of the observed dataset (and of equal size to the observed dataset).

It may also be used for constructing hypothesis tests. It is often used as an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors.

The bootstrap was published by Bradley Efron in “Bootstrap methods: another look at the jackknife” (1979). It was inspired by earlier work on the jackknife. Improved estimates of the variance were developed later. A Bayesian extension was developed in 1981. The bias-corrected and accelerated (BCa) bootstrap was developed by Efron in 1987, and the ABC procedure in 1992.

The basic idea of bootstrapping is that inference about a population from sample data (sample › population) can be modeled by resampling the sample data and performing inference on (resample › sample). As the population is unknown, the true error in a sample statistic against its population value is unknowable. In bootstrap-resamples, the ‘population’ is in fact the sample, and this is known; hence the quality of inference from resample data › ‘true’ sample is measurable.

More formally, the bootstrap works by treating inference of the true probability distribution J, given the original data, as being analogous to inference of the empirical distribution of J, given the resampled data. The accuracy of inferences regarding J using the resampled data can be assessed because we know J. If J is a reasonable approximation to J, then the quality of inference on J can in turn be inferred.

As an example, assume we are interested in the average (or mean) height of people worldwide. We cannot measure all the people in the global population, so instead we sample only a tiny part of it, and measure that. Assume the sample is of size N; that is, we measure the heights of N individuals. From that single sample, only one estimate of the mean can be obtained. In order to reason about the population, we need some sense of the variability of the mean that we have computed. The simplest bootstrap method involves taking the original data set of N heights, and, using a computer, sampling from it to form a new sample (called a ‘resample’ or bootstrap sample) that is also of size N. The bootstrap sample is taken from the original using sampling with replacement so, assuming N is sufficiently large, for all practical purposes there is virtually zero probability that it will be identical to the original “real” sample. Since we are sampling with replacement, we are likely to get one element repeated, and thus every unique element be used for each resampling. This process is repeated a large number of times (typically 1,000 or 10,000 times), and for each of these bootstrap samples we compute its mean (each of these are called bootstrap estimates). We now have a histogram of bootstrap means. This provides an estimate of the shape of the distribution of the mean from which we can answer questions about how much the mean varies. (The method here, described for the mean, can be applied to almost any other statistic or estimator.)

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