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On dual empirical likelihood inference under semiparametric density ratio models in the presence of multiple samples with applications to long term monitoring of lumber quality Cai, Song


Maintaining a high quality of lumber products is of great social and economic importance. This thesis develops theories as part of a research program aimed at developing a long term program for monitoring change in the strength of lumber. These theories are motivated by two important tasks of the monitoring program, testing for change in strength populations of lumber produced over the years and making statistical inference on strength populations based on Type I censored lumber samples. Statistical methods for these inference tasks 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 as the tool for statistical inference. We develop a dual empirical likelihood ratio test for composite hypotheses about the parameter of the density ratio model based on independent samples from different populations. This test encompasses testing differences in population distributions as a special case. We find the proposed test statistic to have a classical chi-square null limiting distribution. We also derive the power function of the test under a class of local alternatives. It reveals that the local power 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. We also establish a powerful inference framework for performing empirical likelihood inference under the density ratio model when Type I censored samples are present. This inference framework centers on the maximization of a concave dual partial empirical likelihood function, and features an easy computation. We study the properties of this dual partial empirical likelihood, and find its corresponding likelihood ratio test to have a simple chi-square limiting distribution under the null model and a non-central chi-square limiting distribution under local alternatives.

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