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On Using Truncated Sequential Probability Ratio Test Boundaries for Monte Carlo Implementation of Hypothesis Tests.
Michael P Fay1, Hyune-Ju Kim, Mark Hachey
1National Institute of Allergy and Infectious Diseases, 6700B Rockledge Drive MSC 7609, Bethesda, MD 20892-7609.
Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|July 18, 2008
Summary
Sequential stopping boundaries for Monte Carlo (MC) hypothesis tests significantly reduce computation time. This study introduces a valid p-value and confidence intervals using a truncated sequential probability ratio test (SPRT) algorithm.
Area of Science:
- Computational Statistics
- Statistical Hypothesis Testing
Background:
- Monte Carlo (MC) hypothesis tests can be computationally intensive.
- Sequential stopping boundaries offer a method to reduce computation time by stopping resampling early.
Purpose of the Study:
- To develop and evaluate a tractable algorithm for implementing truncated sequential probability ratio test (SPRT) boundaries in MC hypothesis tests.
- To ensure the validity of p-values and minimize resampling risk when using sequential boundaries.
- To recommend specific SPRT boundaries that are minimax with respect to resampling risk.
Main Methods:
- Implementation of a truncated sequential probability ratio test (SPRT) boundary algorithm.
- Analysis of p-value validity and resampling risk (RR) for sequential boundaries.
- Comparison of RR for SPRT boundaries against fixed boundaries.
- Development of a new valid p-value estimator for recommended boundaries.
Main Results:
- A tractable algorithm for truncated SPRT boundaries is provided, enabling calculation of valid p-values and confidence intervals.
- A class of SPRT boundaries is identified as minimax regarding resampling risk.
- Recommended truncated SPRT boundaries demonstrate favorable resampling risk compared to fixed boundaries.
- A new, simple, valid p-value estimator is proposed for the recommended boundaries.
Conclusions:
- Sequential stopping boundaries, specifically truncated SPRT boundaries, offer an efficient method for MC hypothesis testing.
- The proposed algorithm and valid p-value estimator enhance the practical application of these methods.
- The MChtest R package is available to implement these computational and statistical advancements.
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