Hands-On Simulation Modeling with Python by Giuseppe Ciaburro

Author:Giuseppe Ciaburro
Language: eng
Format: epub
Publisher: Packt Publishing Pvt Ltd
Published: 2020-07-16T00:00:00+00:00

Bootstrap definition problem

Bootstrap is a statistical resampling technique with reentry so that we can approximate the sample distribution of a statistic. It therefore allows us to approximate the mean and variance of an estimator so that we can build confidence intervals and calculate test p-values when the distribution of the statistics of interest is not known.

Important Note

Bootstrap is based on the fact that the only available sample is used to generate many more samples and to build the theoretical reference distribution. Use the data from the original sample to calculate a statistic and estimate its sample distribution without making any assumptions about the distribution model.

The plug-in principle is used to generate the distribution; that is, the estimate of θ is constructed by substituting the empirical equivalent of the unknown distribution function of the population. The distribution function of the sample is obtained by constructing a distribution of frequencies of all the values it can assume in that experimental situation.

In the simple case of simple random sampling, the operation is as follows. Consider an observed sample with n elements, as described by the following equation:

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