Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

CHARACTERIZATION AND THERMAL-HYDRAULIC MODELING OF ENGINEERED BARRIERS FOR A CANADIAN DEEP GEOLOGICAL REPOSITORY FOR USED NUCLEAR FUEL

Within Canada there are more than 2.5 million bundles of spent nuclear fuel with another approximately 2 million bundles to be generated in the future. Canada, and every country around the world that has taken a decision on management of spent nuclear fuel, has decided on long-term containment and isolation of the fuel within a deep geological repository. At depth, a deep geological repository consists of a network of placement rooms where the bundles will be located within a multi-layered system that incorporates engineered and natural barriers. The barriers will be placed in a complex thermal-hydraulic-mechanical-chemical-biological (THMCB) environment. A large database of material properties for all components in the repository are required to construct representative models. Within the repository, the sealing materials will experience elevated temperatures due to the thermal gradient produced by radioactive decay heat from the waste inside the container. Furthermore, high porewater pressure due to the depth of repository along with possibility of elevated salinity of groundwater would cause the bentonite-based materials to be under transient hydraulic conditions. Therefore it is crucial to characterize the sealing materials over a wide range of thermal-hydraulic conditions. A comprehensive experimental program has been conducted to measure properties (mainly focused on thermal properties) of all sealing materials involved in Mark II concept at plausible thermal-hydraulic conditions. The thermal response of Canada’s concept for a deep geological repository has been modelled using experimentally measured thermal properties. Plausible scenarios are defined and the effects of these scenarios are examined on the container surface temperature as well as the surrounding geosphere to assess whether they meet design criteria for the cases studied. The thermal response shows that if all the materials even being at dried condition, repository still performs acceptably as long as sealing materials remain in contact.