Semiparametric monitoring test based on clustered data

Joint work with Pengfei Li and  Yukun Liu

Part of the Forestry Product Project headed by Jim Zidek

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Due to factors such as climate change, forest fire and plague of insects, it is essential to update lumber quality monitoring procedures in American Society for Testing and Materials (ASTM) Standard D1990 (adopted in 1991) from time to time. A key component of monitoring is an effective method for detecting the change in lower percentiles of the solid lumber strength based on observations of multiple samples. Yet currently used statistical methods do not meet the modern standard of high sensitivity and reliability, particularly when the data are clustered.

In a recent study by Verrill et al. (2015), eight statistical tests proposed by wood scientists were examined thoroughly based on real and simulated data sets. They are found unsatisfactory for various reasons such as seriously inflated false alarm rate when observations are clustered, suboptimal power properties, or having ad hoc rejection regions. The ultimate reason behind the unsatisfactory performance is that most of these tests are developed for purposes other than detecting the changes in quantile.

This paper proposes a method directly targeting changes in quantile based on a composite empirical likelihood. The approach effectively combines the information from multiple samples via a semi-parametric model assumption. It satisfactorily controls the type I error through a cluster-based bootstrapping procedure whether or not the data are correlated. The performance of the test is examined through simulation experiments and a real data example. The new method is generic, not confined to the motivating example.