Fiducial Inference on the Largest Mean of a Multivariate Normal Distribution
Damian Wandler, CSU, PhD Graduate Student
Thursday, October 8, 2009
12:00 p.m., 223 Weber
We propose an inference procedure for the value of the largest mean of a multivariate normal distribution. This problem is surprisingly difficult and relatively unexplored; especially in the case when there could be more than one of the means equal to the largest mean. Our proposed solution is based on an extension of R. A. Fisher's fiducial inference methods termed generalized fiducial inference. We use the generalized fiducial distribution to find confidence intervals and study their properties both theoretically and by simulations. We show that the proposed confidence intervals have asymptotically correct frequentist coverage and possess promising small sample empirical properties. Additionally, our method is also applied to the air quality index of the four largest cities in the northeastern United States (Baltimore, Boston, New York, and Philadelphia).