Block bootstrap Bootstrapping (statistics)

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1 block bootstrap

1.1 time series: simple block bootstrap
1.2 time series: moving block bootstrap
1.3 cluster data: block bootstrap





block bootstrap

the block bootstrap used when data, or errors in model, correlated. in case, simple case or residual resampling fail, not able replicate correlation in data. block bootstrap tries replicate correlation resampling instead blocks of data. block bootstrap has been used data correlated in time (i.e. time series) can used data correlated in space, or among groups (so-called cluster data).


time series: simple block bootstrap

in (simple) block bootstrap, variable of interest split non-overlapping blocks.


time series: moving block bootstrap

in moving block bootstrap, introduced künsch (1989), data split n-b+1 overlapping blocks of length b: observation 1 b block 1, observation 2 b+1 block 2 etc. these n-b+1 blocks, n/b blocks drawn @ random replacement. aligning these n/b blocks in order picked, give bootstrap observations.


this bootstrap works dependent data, however, bootstrapped observations not stationary anymore construction. but, shown varying randomly block length can avoid problem. method known stationary bootstrap. other related modifications of moving block bootstrap markovian bootstrap , stationary bootstrap method matches subsequent blocks based on standard deviation matching.


cluster data: block bootstrap

cluster data describes data many observations per unit observed. observing many firms in many states, or observing students in many classes. in such cases, correlation structure simplified, , 1 make assumption data correlated group/cluster, independent between groups/clusters. structure of block bootstrap obtained (where block corresponds group), , groups resampled, while observations within groups left unchanged. cameron et al. (2008) discusses clustered errors in linear regression.








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