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Article: Efficient computation of multivariate empirical distribution functions at the observed values
Title | Efficient computation of multivariate empirical distribution functions at the observed values |
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Authors | |
Keywords | Integral evaluation Joint probabilities Monte Carlo simulation Sorting algorithms |
Issue Date | 2018 |
Publisher | Springer. The Journal's web site is located at http://www.springer.com/statistics/journal/180 |
Citation | Computational Statistics, 2018, v. 33 n. 3, p. 1413-1428 How to Cite? |
Abstract | Consider the evaluation of model-based functions of cumulative distribution functions that are integrals. When the cumulative distribution function does not have a tractable form but simulation of the multivariate distribution is easily feasible, we can evaluate the integral via a Monte Carlo sample, replacing the model-based distribution function by the empirical distribution function. Given a simulation sample of size N, the naive method uses O(N^2) comparisons to compute the empirical distribution function at all N sample vectors. To obtain faster computational speed when N needs to be large to achieve a desired accuracy, we propose methods modified from the popular merge sort and quicksort algorithms that preserve their average O(N*logN) complexity in the bivariate case. The modified merge sort algorithm can be extended to the computation of a d-dimensional empirical distribution function at the observed values with O(N*(logN)^(d-1)) complexity. Simulation studies suggest that the proposed algorithms provide substantial time savings when N is large. |
Persistent Identifier | http://hdl.handle.net/10722/259497 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.566 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lee, D | - |
dc.contributor.author | Joe, H | - |
dc.date.accessioned | 2018-09-03T04:08:47Z | - |
dc.date.available | 2018-09-03T04:08:47Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Computational Statistics, 2018, v. 33 n. 3, p. 1413-1428 | - |
dc.identifier.issn | 0943-4062 | - |
dc.identifier.uri | http://hdl.handle.net/10722/259497 | - |
dc.description.abstract | Consider the evaluation of model-based functions of cumulative distribution functions that are integrals. When the cumulative distribution function does not have a tractable form but simulation of the multivariate distribution is easily feasible, we can evaluate the integral via a Monte Carlo sample, replacing the model-based distribution function by the empirical distribution function. Given a simulation sample of size N, the naive method uses O(N^2) comparisons to compute the empirical distribution function at all N sample vectors. To obtain faster computational speed when N needs to be large to achieve a desired accuracy, we propose methods modified from the popular merge sort and quicksort algorithms that preserve their average O(N*logN) complexity in the bivariate case. The modified merge sort algorithm can be extended to the computation of a d-dimensional empirical distribution function at the observed values with O(N*(logN)^(d-1)) complexity. Simulation studies suggest that the proposed algorithms provide substantial time savings when N is large. | - |
dc.language | eng | - |
dc.publisher | Springer. The Journal's web site is located at http://www.springer.com/statistics/journal/180 | - |
dc.relation.ispartof | Computational Statistics | - |
dc.rights | This is a post-peer-review, pre-copyedit version of an article published in [Computational Statistics]. The final authenticated version is available online at: https://doi.org/10.1007/s00180-017-0771-x | - |
dc.subject | Integral evaluation | - |
dc.subject | Joint probabilities | - |
dc.subject | Monte Carlo simulation | - |
dc.subject | Sorting algorithms | - |
dc.title | Efficient computation of multivariate empirical distribution functions at the observed values | - |
dc.type | Article | - |
dc.identifier.email | Lee, D: leedav@hku.hk | - |
dc.identifier.authority | Lee, D=rp02276 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1007/s00180-017-0771-x | - |
dc.identifier.scopus | eid_2-s2.0-85031501298 | - |
dc.identifier.hkuros | 288840 | - |
dc.identifier.volume | 33 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 1413 | - |
dc.identifier.epage | 1428 | - |
dc.identifier.isi | WOS:000436998200015 | - |
dc.publisher.place | Germany | - |
dc.identifier.issnl | 0943-4062 | - |