Multi-Parameter One-Sided Monitoring Tests

ABSTRACT

Multi-parameter one-sided hypothesis test problems arise naturally in many applications. We are particularly interested in effective tests for monitoring multiple quality indices in forestry products. Our search reveals that there are many effective statistical methods in the literature for normal data, and that they can easily be used to test hypotheses regarding parameter values permitting asymptotically normal estimators. We find that the classical likelihood ratio test is unsatisfactory, because to control the size, it must cope with the least favorable distributions at the cost of power. In this article, we find a novel way to slightly ease the size control, obtaining a much more powerful test. Simulation confirms that the new test retains good control of the Type I error and is markedly more powerful than the likelihood ratio test as well as many competitors based on normal data. The new method performs well in the context of monitoring multiple quality indices.

KEYWORDS:

• Bootstrap
• Composite likelihood
• Density ratio model
• Empirical likelihood
• Multiple sample
• Random effect

Acknowledgments

The authors gratefully acknowledge funding from National Natural Science Foundation of China Grant No. 11690011 and NSERC Grant RGPIN-2014-03743, and a Collaborative Research and Development Grant from NSERC and FPInnovations. The authors are also indebted to the Forest Products Stochastic Modelling Group centered at the University of British Columbia (UBC): members of this group from FPInnovations in Vancouver, Simon Fraser University, and UBC provided stimulating discussions of the long-term monitoring program to which this article contributes.

Additional information

Funding

National Natural Science Foundation of China(11690011, 10.13039/501100001809), NSERC(RGPIN-2014-03743)