|Application of Fiducial Inference
| Lidong E
Ph.D. Candidate, Colorado State University, Department of Statistics
Wednesday, March 7, 2007
Hannig (2006) 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 (FGPQ) to make inference in four practical problems. The list of problems we consider is
Simultaneous Confidence Intervals for Ratios of Means of Lognormal Distributions. In this work, we propose a new method for constructing simultaneous confidence intervals for all pairwise ratios of means of lognormal distributions. Our approach is based on Fiducial Generalized Pivotal Quantities (FGPQ) for vector parameters. Simulation studies show that the constructed intervals have satisfactory small sample performance. We also prove that they have correct asymptotic coverage. The result has application in bioequivalence studies for comparing three or more drug formulations.
Confidence Intervals for Variance Components in an Unbalanced Two-component normal Mixed Linear Model. In this work, a new method for constructing confidence intervals for between group variance, within group variance and the intraclass correlation in a two-component mixed effects linear model is proposed based on the fiducial recipe. A simulation study is conducted to compare the resulting interval estimates with other competing confidence interval procedures from the literature. Our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability. In addition these intervals have shorter average confidence interval lengths overall. We also prove that these fiducial intervals have asymptotically exact frequentist coverage probability. The computations for the proposed procedures are illustrated using examples from animal breeding applications.
Confidence Intervals for Median Lethal Dose (LD50) (future work). In this work, we'll propose a new method for constructing confidence intervals of LD50 for a logistic-response curve based on the fiducial recipe. The properties of the constructed confidence intervals will be studied.
Confidence Intervals for the Concordance Correlation Coefficient (CCC) and the Assessment of Agreement (future work). In this work, we'll develop a Fiducial Generalized Confidence Interval (FGCI) for the concordance correlation coefficient proposed by Lin (1989, 1992) to quantify agreement between two methods of measurement. We will use the proposed FGCI to conduct statistical tests. The properties of the constructed confidence intervals will be studied.