Bootstrap – a statistical method

In this section, we will explore complex statistical functional. What is the statistical distribution of the correlation between two random variables? If normality assumption does not hold for the multivariate data, then what is an alternative way to obtain the standard error and confidence interval? Efron (1979) invented the bootstrap technique, which provides the solutions that enable statistical inference related to complex statistical functionals. In Chapter 1, Introduction to Ensemble Techniques, the permutation test, which repeatedly draws samples of the given sample and carries out the test for each of the resamples, was introduced. In theory, the permutation test requires number of resamples, where m and n are the number of observations in the two samples, though one does take their foot off the pedal after having enough resamples. The bootstrap method works in a similar way and is an important resampling method.

Let be an independent random sample...