Optimal generalized truncated sequential Monte Carlo test.
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Data
2013
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Resumo
When it is not possible to obtain the analytical null distribution of a test statistic
U, Monte Carlo hypothesis tests can be used to perform the test. Monte Carlo tests
are commonly used in a wide variety of applications, including spatial statistics, and
biostatistics. Conventional Monte Carlo tests require the simulation of m independent
copies from U under the null hypothesis, what is computationally intensive for large data
sets. Truncated sequential Monte Carlo designs can be performed to reduce computational
effort in such situations. Different truncated sequential procedures have been proposed.
They work under restrictive assumptions on the distribution of U aiming to bound the
power loss and to reduce execution time. Since the use of Monte Carlo tests are based
on the situations where the null distribution of U is unknown, their results are not valid
for the general case of any test statistic. In this paper, we derive an optimal scheme for
truncated sequential Monte Carlo hypothesis tests. This scheme minimizes the expected
number of simulations under any alternative hypothesis, and bounds the power loss in
arbitrarily small values. The first advantage from this scheme is that the results concerning
the power and the expected time are valid for any test statistic. Also, we present practical
examples of optimal procedures for which the expected number of simulations are reduced
by 60% in comparison with some of the best procedures in the literature.
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Execution time, Power loss, p-value density, Resampling risk
Citação
SILVA, I. R.; ASSUNÇÃO, R. M. Optimal generalized truncated sequential Monte Carlo test. Journal of Multivariate Analysis, v. 121, p. 33-49, 2013. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0047259X13001152>. Acesso: 13 abr. 2015.