This thesis provides several new calibration methods for the empirical log-likelihood ratio. The commonly used Chi-square calibration is based on the limiting distribu¬tion of this ratio but it constantly suffers from the undercoverage problem. The finite sample distribution of the empirical log-likelihood ratio is recognized to have a mix¬ture structure with a continuous component on [0, +∞) and a probability mass at +∞. Consequently, new calibration methods are developed to take advantage of this mixture structure; we propose new calibration methods based on the mixture distrib¬utions, such as the mixture Chi-square and the mixture Fisher's F distribution. The E distribution introduced in Tsao (2004a) has a natural mixture structure and the calibration method based on this distribution is considered in great details. We also discuss methods of estimating the E distributions.