Abstract
Since their introduction by Dwass (1957) and Barnard (1963), Monte Carlo tests have attracted considerable attention. The aim of this paper is to give a unified approach that covers the case of an arbitrary null distribution in order to study the statistical properties of Monte Carlo tests under the null hypothesis and under the alternative. For finite samples we obtain bounds for the power of the Monte Carlo test with the original test that allow determination of the required simulation effort. Furthermore the concept of asymptotic (resp. local asymptotic) relative Pitman efficiency (ARPE, resp. LARPE) is adapted to Monte Carlo tests for the study of their asymptotic behaviour. The normal limit case is investigated in more detail, leading to explicit formulas for ARPE and LARPE.
Keywords
Monte Carlo methodNull (SQL)Applied mathematicsNull hypothesisMonte Carlo method in statistical physicsMathematicsStatistical physicsStatistical hypothesis testingMonte Carlo integrationNull distributionMonte Carlo molecular modelingQuasi-Monte Carlo methodLimit (mathematics)Hybrid Monte CarloComputer scienceStatisticsPhysicsMarkov chain Monte CarloTest statisticMathematical analysis
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Publication Info
- Year
- 1986
- Type
- article
- Volume
- 14
- Issue
- 1
- Citations
- 159
- Access
- Closed
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Cite This
Karl‐Heinz Jöckel
(1986).
Finite Sample Properties and Asymptotic Efficiency of Monte Carlo Tests.
The Annals of Statistics
, 14
(1)
.
https://doi.org/10.1214/aos/1176349860
Identifiers
- DOI
- 10.1214/aos/1176349860