Sequential Sampling to Construct Confidence Regions for an Unknown Mean Vector

Thomas M. Menino Convention & Exhibition Center 

Traditional fixed-size confidence region (FSCR) methods for estimating the mean of a multivariate normal distribution often fix the region's maximum diameter in advance, without regard to the quality of available data. We propose a new approach that incorporates data quality into determining the region's size. Starting with a modified FSCR method where the structure of the variance-covariance matrix is known, we introduce a minimum risk FSCR (MRFSCR) framework inspired by point estimation methods that balance estimation accuracy and sampling cost. We develop a unified multistage sampling strategy to construct these regions, ensuring desirable asymptotic properties. The methodology is illustrated through practical sampling strategies, simulation studies, and real-data examples.

sequential sampling

multivariate analysis

confidence region construction

statistical inference 

Survey Research Methods Section