Fixed diameter confidence ellipsoid in time-sequential models

Abstract

In the context of life testing, when the objective is to estimate a parameter of the survival function, we wish to find a region R in k-dimensional Euclidean space such that P(θ ∊ R) = α and the maximum diameter of R ≤ 2d . This goal cannot be achieved by utilizing the accumulated data from a sample up to a fixed time t . Hence we will consider time-sequential procedure where we will observe the process up to a stopping time γ(E γ_d) and then construct the region R with maximum diameter 2d which includes θ with probability approximately equal to α.

Keywords:

• censored data
• likelihood process
• counting process
• score process
• stopping times