Mutshinda Crispin

Coverage Accuracy of Confidence Intervals for Parameters and Quantiles in Extreme Value Distributions



Abstract

Explicit expressions for information matrices are known for extreme
value distributions. In order to construct confidence intervals for
parameters and quantiles in extreme value distributions, one can use
either the inverse of the expected or the observed information
matrix. Since the common practice is the use of the observed
information matrix, an extensive simulation study is needed to compare
performances of these two methods in constructing confidence intervals
for parameters and quantiles with different sample sizes and different
shape parameters.  In this thesis we report on a simulation study
designed to compare the performance of these methods in terms of
coverage accuracy of intervals each method generates. The performance
of the profile likelihood method is examined as well.   Keywords:
Extreme Value Distributions, Expected Information Matrix, Observed
Information Matrix, Profile likelihood, Coverage of confidence
intervals.