Using massively parallel processing in the testing of the robustness of statistical tests with Monte Carlo simulation
In this paper, we will examine the application of the Monte Carlo method in the testing of the robustness of statistical tests. The very computation-intensive Monte Carlo testing was implemented using the so-called GP-GPU method, which utilises the video cards’ GPU (Graphical Processing Unit) to per...
Elmentve itt :
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| Dokumentumtípus: | Könyv része |
| Megjelent: |
2010
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| Sorozat: | Proceedings of the Challenges for Analysis of the Economy, the Businesses, and Social Progress : International Scientific Conference Szeged, November 19-21, 2009
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| Kulcsszavak: | Statisztika - módszertan, Monte Carlo módszer |
| Online Access: | http://acta.bibl.u-szeged.hu/57875 |
| Tartalmi kivonat: | In this paper, we will examine the application of the Monte Carlo method in the testing of the robustness of statistical tests. The very computation-intensive Monte Carlo testing was implemented using the so-called GP-GPU method, which utilises the video cards’ GPU (Graphical Processing Unit) to perform the necessary calculations. The robustness of a statistical test is defined as its property to remain valid even if its assumptions are not met. (We call a test valid if its significance level is equal to its Type I Error Rate.) One way to investigate the robustness of a statistical test (especially useful if the test’s complicated structure makes analytic handling infeasible or impossible) is to employ the so-called Monte Carlo method. Here, we generate many random samples (meeting or violating the assumptions, which we can arbitrarily set), perform the statistical test many times on them, and then check whether the empirically found Type I Error Rate converges to the specified significance level or not. This way, we give up exactness for the complete insensitivity to the complexity of the examined statistical test. This method (by requiring enormous amount of random number generations and statistical testings for reliable results) is very computation-intensive; traditionally only supercomputers could be used effectively, limiting the availability of this method. However a new approach, called GP-GPU, makes it possible to harness the extremely high computing performance of – even ordinary, widely available – video cards found in every modern PC. We implemented a framework that performs the abovementioned MC-testing of the robustness of statistical tests. We call our program “framework”, because it can be easily expanded with virtually any statistical test (to which no GP-GPU knowledge is needed), and be tested with very high performance – even with widely available tools. As an example, we performed the analysis of the well known Student’s t-test; and – using this as a starting point – we demonstrated the main advantages of our framework. |
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| Terjedelem/Fizikai jellemzők: | 1343-1366 |
| ISBN: | 978-963-06-9558-9 |