Confidence intervals constructed from a fixed-sample size procedure may sometimes be too wide to be of any practical use. Hence, to avoid such a problem, it is desirable to construct confidence intervals with fixed-width. G. B. Dantzig (1940) showed that there did not exist any fixed sample size procedure which produces fixed-width confidence interval with a prescribed confidence level. Charles Stein (1945, 1949) introduced the groundbreaking idea of sampling in two stages to construct fixed-width confidence intervals with a prescribed confidence level. In this talk, we consider the problem of fixed-width interval estimation of normal mean with unknown variance. In doing so, we develop Stein’s two-stage procedure and successively go through its modifications leading to modified two stage and purely sequential procedures. We also discuss properties associated with these procedures and how they compare with each other. If time permits we will also consider the problem of fixed-width interval estimation of a p dimensional normal mean vector with a certain structure for the dispersion matrix.
SMS seminar room
4th Year student, SMS, NISER
Some Topics in Sequential Estimation