Open Collections

Abstract

Quantiles and their functions are important population characteristics in many applications. In forestry, lower quantiles of the modulus of rapture and other mechanical properties of the wood products are important quality indices. It is important to ensure that the wood products in the market over the years meet the established industrial standards. Two well-known risk measures in finance and hydrology, value at risk (VaR) and median shortfall (MS), are quantiles of their corresponding marginal distributions. Developing effective statistical inference methods and tools on quantiles of interest is an important task in both theory and applications. When samples from multiple similar natured populations are available, Chen et al. [2016] proposed to use a density ratio model (DRM) to characterize potential latent structures in these populations. The DRM enables us to fully utilized the information contained in the data from connected populations. They further proposed a composite empirical likelihood (CEL) to avoid a parametric model assumption that is subject to model-mis-specification risk and to accommodate clustered data structure. A cluster-based bootstrap procedure was also investigated for variance estimation, construction of confidence interval and test of various hypotheses. This thesis contains complementary developments to Chen et al. [2016]. First, a user-friendly R package is developed to make their methods easy-to-use for practitioners. We also include some diagnostic tools to allow users to investigate the goodness of the fit of the density ratio model. Second, we use simulation to compare the performance DRM-CEL-based test and the famous Wilcoxin rank test for clustered data. Third, we study the performance of DRM-CEL-based inference when the data set contains observations with different cluster sizes. The simulation results show that DRM-CEL method works well in common situations.