Hypothesis testing under density ratio models in the presence of Type I censored multiple samples

Maintaining a high quality of lumber products is of great social and economic importance. As part of a research program aimed at developing a long term program for monitoring change in the strength of lumber, we develop a theory of hypothesis testing concerning a given number of populations with Type I censored samples from each. Statistical methods for lumber quality monitoring should ideally be efficient and nonparametric. These desiderata lead us to adopt a semiparametric density ratio model to pool the information across multiple samples and use the nonparametric empirical likelihood (EL) as the tool for statistical inference. We establish a powerful framework for performing EL inference under the density ratio model when Type I censored samples are present. This inference framework centers on a concave dual partial EL, and features an easy computation. We find that under a class of general composite hypotheses, the corresponding EL ratio test has a classical chi--square limiting distribution under the null model and a non--central chi--square limiting distribution under local alternatives. We show that the local power of this EL ratio test is often increased when strength is borrowed from additional samples even when their underlying distributions are unrelated to the hypothesis of interest. Simulation studies show that this test has better power properties than all potential competitors adopted to the multiple sample problem under the investigation, and is robust to model misspecification. The proposed test is then applied to assess strength properties of lumber with intuitively reasonable implications for the forest industry.