Multiple crossing sequential fixed-size confidence region methodologies for a multivariate normal mean vector

The asymptotically efficient and asymptotically consistent   purely sequential procedure of Mukhopadhyay and Al-Mousawi (1986) is customarily used to construct a confidence region RR for the mean vector μ of Np(μ,σ2H). This procedure does not have the exact consistency   property. Hp×p is assumed known and positive definite with σ2σ2 unknown. The maximum diameter of RR and the confidence coefficient are prefixed.A purely sequential sampling strategy is proposed allowing sampling until sample size crosses the boundary multiple times. We ascertain asymptotic efficiency and asymptotic consistency properties (Theorem 3.1). Its ability to nearly achieve required coverage probability without significant over-sampling is demonstrated with simulations. A truncation technique plus fine-tuning of the multiple crossing rule are proposed to increase practicality. Two real data illustrations are highlighted.