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Jackknife, Bootstrap and Other Resampling Methods - Statswork

Resampling at Statswork

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Resampling is a revolutionary methodology as it departs from theoretical distribution. The inference is purely based on repeated sampling within the same sample and does not emerge without any context. In general, resampling is tied to the Monte Carlo simulation where researchers make up data and draw conclusions based on the possible scenarios. However, there is a huge difference and similarities between Monte Carlo simulation and resampling where later one could do all possible combinations but time consuming and intensive while the former restricts the resampling to a certain number. Further, Monte Carlo is totally hypothetical while in the latter simulation is based on real data.

 

There are at least five types of resampling and they are as follows

  • Monte Carlo Simulation
  • Randomization exact test or the permutation test (RA Fisher, 1935/1960)
  • Cross Validation – Kurtz (1948)
  • Jackknife or the Quenouille-Tukey Jackknife (Maurice Quenouille, 1949)
  • Bootstrap – Bradley Efron (1979, 1981, 1982)

Application of resampling

  • Analysis of Null models, competition, and community structure
  • Detecting Density Dependence
  • Characterizing Spatial Patterns and Processes
  • Estimating Population Size and Vital Rates
  • Environmental Modeling
  • Evolutionary Processes and Rates
  • Phylogeny Analysis

Information input for resampling method.

The Flow of Information for resampling methods
Specify
  • The universe to sample from (random numbers),
  • The sampling procedure (number, sizes of samples, sampling with or without replacement),
  • and the statistic.
Information flow.
  • Input data
  • Resample from the inputted data
  • Calculate the statistic desired
  • Record statistic
  • Return to sample for (X) number of resamples; once reached to completed (X) times, continue to step 6
  • Calculate p-value by counting number of resamples that occur in desired extreme domains divided by the total number of resamples
  • Present/Print results

The size and complexity of a model dictates the number of iterations needed in a given simulation. By keeping track of the stability of the output distributions being generated, it is possible to determine the adequate number of iterations required. Typically, output distributions become more stable as the number of iterations per simulation is increased. This is because as the sample size increases and the distribution change less. The simulation process may be stopped when the statistics change less than a percentage of the convergence (e.g. 15). The parameters considered for this test are the standard deviation, the mean and the percentiles ( 5% to 95% in 5% increments) of each output.

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Resampling Computer Programs

The following program to calculate resampling
  • R – a programming language, easy to manipulate. The program is free and scripts are precompiled throughout the Internet.
  • C++ – like R, this is a programming language.
  • Resampling Stats – easy to use, this programming language seems very like BASIC programming language. It has all the resampling method functions already incorporated and is also available as a Microsoft Excel add-in.
  • S Plus – R based, this program has many built-in functions and pull-down menus.
  • SAS – commonly used in statistical analysis, this package is C based.
  • SPSS

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