Sequential approach to simultaneous estimation of the mean and variance

The problem of simultaneous estimation of the mean and variance of a normal distribution has been studied. We propose a semi-circular region _n ={(a,b)':b>0} of radiusd, which has approximately a preassigned coverage probability. Asymptotic efficiency and asymptotic consistency (asd0) of our proposed sequential procedures have been proved.Research partially supported by U.S. Army Research Grant No. DAAG29-76-G-0038.