NATURAL AND MODIFIED CONJUGATE PRIORS IN EXPONENTIAL
FAMILIES OF STOCHASTIC PROCESSES
Ryszard Magiera
Maciej Wilczyński
Abstract: Modified conjugate families of prior distributions are investigated and their
properties are examined in the context of applications to admissible and minimax estimation
for the general exponential model for stochastic processes defined by (1). The conjugate
priors are characterized as those which yield a linear admissible estimator under a weighted
quadratic loss in a sequential statistical model. In Section 3, a new characterization of
conjugate priors is presented which is relevant to the problem of finding minimax estimators
in the statistical model that after a random time transformation cannot be reduced to a model
for processes with stationary independent increments. Applications of the results
obtained are presented in some special models, among others to a zero mean stationary
Gaussian Markov process in the problem of estimating the variance parameter.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -