The thesis deals with the competing risks model with
independent
exponential distributions of risks, the natural conjugate prior
and three its generalizations are considered for parameters of
the model.
Bayes estimators under the quadratic loss function are explored.
Their convergence and asymptotic normality (including the weak
asymptotics of the reliability function estimator considered as a
process in C[0,\infty]) are given and Bayes risks (and the integrated
Bayes risk), or at least their asymptotic expansion, are derived.
The latter are used to measure sensitivity of the estimators to
changes in the prior density by asymptotic deficiency.
The results are generalized to a multiple-state model with
constant transition intensities (a homogeneous Markov process).
The Koziol-Green model of random censorship is presented as a
special case, models with more general forms of intensities are
discussed.
An appendix provides a proposition suitable for asymptotic
expansion of functions of random variables by means of
conditional moments. |