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Subject 3. Bootstrapping and Empirical Sampling Distributions PDF Download

Bootstrapping and resampling are statistical techniques used to estimate parameters and assess the uncertainty associated with a sample or population.

Bootstrapping is a resampling technique that involves creating multiple new samples, known as bootstrap samples, by drawing observations from the original sample with replacement. It allows for estimating the sampling distribution of a statistic without assuming a specific underlying probability distribution.

The basic steps involved in bootstrapping are as follows:
  1. Select a random sample of size n from the original sample, with replacement.
  2. Calculate the desired statistic of interest for this bootstrap sample.
  3. Repeat steps a and b multiple times (typically a large number of iterations, such as 1,000 or 10,000).
  4. Analyze the distribution of the computed statistics to estimate confidence intervals or construct hypothesis tests.

Bootstrapping can be useful for estimating parameters, such as the mean, standard deviation, or correlation, and for constructing confidence intervals or conducting hypothesis tests when the underlying distribution is unknown or not easily specified.

Resampling is a more general term that includes various techniques, including bootstrapping. In addition to bootstrapping, two other commonly used resampling techniques are:

  • The Jackknife works by sequentially deleting one observation in the data set, then recomputing the desired statistic. It is computationally simpler than bootstrapping. It can be used for bias correction, variance estimation, and hypothesis testing.

    The jackknife requires n repetitions for a sample of n (for example, if you have 10,000 items then you'll have 10,000 repetitions), while the bootstrap requires "B" repetitions. This leads to a choice of B, which isn't always an easy task.

  • Cross-validation is a resampling technique commonly used in machine learning and predictive modeling.

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