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Iction distributions of reserves produced by the Munich chain ladder (MCL) model. The MCL model was introduced by Quarg and Mack (2004) and takes into account both paid and incurred claims information. In order to produce bootstrap distributions, this paper addresses the application of bootstrapping methods to dependent data, with the consequence that correlations are considered. Numerical examples are provided to illustrate the algorithm and the prediction errors are compared for the new bootst.
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Cij FAQ
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Bootstrap Standard Error: Take k repeated samples with replacement from a given dataset. For each sample, calculate the standard error: s/√n. This results in k different estimates for the standard error. To find the bootstrapped standard error, take the mean of the k standard errors.
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Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates.
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To construct a bootstrap distribution for the mean height we would first randomly select one individual from that sample and record their height. Then, with the that individual placed back into the sample, we would randomly select a second individual and record their height.
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The bootstrap bias estimate (8.13) is the difference between the mean of the bootstrap estimates of θ and the sample estimate of θ . This is similar to the Monte Carlo estimate of bias discussed in Chapter 7.
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Bootstrap Method Choose a number of bootstrap samples to perform. Choose a sample size. For each bootstrap sample. Draw a sample with replacement with the chosen size. Calculate the statistic on the sample. Calculate the mean of the calculated sample statistics.
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Bootstrapping estimates the properties of an estimand (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution function of the observed data.
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Bootstrap techniques provide another means of estimating expected discrepancies which is widely applicable. In the bootstrap method, the unknown distribution Q is replaced by Qn which assigns probability mass 1/n to each observed value xi, i=1,…,n (Efron 1982).
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Bootstrapping methods are a numerical approach to generating confidence intervals that use either resampled data or simulated data to estimate the sampling distribution of the maximum likelihood parameter estimates.
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