Applications of generalized fiducial inference - E, Lidong, author; Iyer, Hariharan K., advisor (Colorado State University. Libraries, 2009)
Hannig (2008) generalized Fisher's fiducial argument and obtained a fiducial recipe for interval estimation that is applicable in virtually any situation. In this dissertation research, we apply this fiducial recipe and fiducial generalized pivotal quantity to make inference in four practical problems. The list of problems we consider is (a) confidence intervals for variance components in an unbalanced two-component normal mixed linear model; (b) confidence intervals for median lethal dose (LD50) in bioassay experiments; (c) confidence intervals for the concordance correlation coefficient (CCC) in method comparison; (d) simultaneous confidence intervals for ratios of means of Lognormal distributions. For all the fiducial generalized confidence intervals (a)-(d), we conducted a simulation study to evaluate their performance and compare them with other competing confidence interval procedures from the literature. We also proved that the intervals (a) and (d) have asymptotically exact frequentist coverage.
Keywords: confidence intervals; fiducial argument; fiducial inference; statistics