Abstract
Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study.
Disciplines
Clinical Trials | Microarrays | Statistical Methodology | Statistical Models | Statistical Theory
Suggested Citation
Uno, Hajime; Tian, Lu; and Wei, L.J., "The Optimal Confidence Region for a Random Parameter" (July 2004). Harvard University Biostatistics Working Paper Series. Working Paper 13.
https://biostats.bepress.com/harvardbiostat/paper13
Included in
Clinical Trials Commons, Microarrays Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons