WITHDRAWN: Tolerance Intervals for Unbalanced Random Two-Fold Nested Models

• Author(s): Tsai-Yu Lin
• Keywords: Generalized confidence interval ; Generalized P-value ; Nested design ; Variance component

Abstract

Tolerance intervals have been widely used in various practical applications. In this paper, we shall extend the results of Liao, Lin and Iyer (2005) to unbalanced random two-fold nested models. Our main interest is to explore procedures for construction of one- and two-sided tolerance intervals for the normal distribution of the observable and the unobservable random variable. The mean and variance of the distribution of interest are estimated using the data from the ANOVA model. The concept of generalized pivotal quantities (GPQs), which have been frequently used to obtain confidence intervals in situations where conventional methods are difficult to apply or fail to provide exact solutions is introduced. Moreover, statistical simulation studies will be conducted to evaluate the frequentist coverage probabilities and expected lengths of the proposed procedure.