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derek_rampal_final - Median Bootstrapping Estimation...

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Median Bootstrapping Estimation Comparison 4/28/2009 Derek Rampal
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Abstract Statistical parameter estimation is fundamental to statistical analysis, but frequently the underlying sampling distribution is unknown. Bootstrapping can serve as a tool to estimate statistical parameters. Different bootstrapping methodologies will be compared to Monte Carlo simulation for differing distributions and the effectiveness compared by the respective average relative error.
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Introduction Given a known population distribution, Monte Carlo sample generation can serve to estimate (accurately) statistical parameters. This is a very effective technique but is extremely limited in that the underlying distribution is required to be known. Unfortunately, because prior knowledge is generally required to know the underlying distribution and this information is frequently unknown, other techniques have been suggested to attempt to estimate the underlying statistical parameters and distribution such as bootstrapping. Bootstrapping is the general term for re-sampling within the original sample space in an attempt to randomize the collected data and determine the convergence of the statistic of interest if there is convergence. There are a variety of techniques which include but are not limited to overlapping and non-overlapping sample collection. Overlapping is an algorithm where re-sampling is accomplished through a series of overlapping samples with size equal to a predetermined block size. Non-overlapping is an algorithm where re-sampling is accomplished through a series of non-overlapping samples with size equal to a predetermined block size. For both algorithms, the newly created overlapping or non-overlapping subsets are randomly sampled and the new bootstrap sample is created by concatenating the respective statistics derived from the sampled subsets. Considering that statistics and statistical analysis relies heavily upon the properties and limitations of the collected samples, distribution bootstrapping is also heavily dependent on the given sample. It is expected by the central limit theorem that by increasing the bootstrap re-sampling sample size, convergence will occur between the bootstrap estimation parameter and the actual unknown population parameters. The ARE (average relative error) will be used to compare respective estimations.
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This note was uploaded on 09/19/2009 for the course MATH compstat taught by Professor Qian during the Spring '09 term at FAU.

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derek_rampal_final - Median Bootstrapping Estimation...

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