Explicit solutions of the Bayes sequential estimation problem for a time-transformed exponential distribution

ABSTRACT

A problem of Bayesian time-sequential estimation of an unknown parameter of a time-transformed exponential distribution is considered. It is supposed that the cost of observing the process is the sum of an increasing function of time and a linear function of the number of observations. Under some general assumptions concerning the loss function associated with the error of estimation, the optimal stopping time is derived using the free-boundary method. As an example, a solution of the problem considered is given in the case of a weighted precautionary loss function.

KEYWORDS:

• Bayes sequential procedure
• free-boundary method
• optimal stopping
• precautionary loss function

SUBJECT CLASSIFICATIONS:

• 62L12
• 62L15
• 62F10
• 62F15