The asymptotic consistency and efficiency of fixed-size sequential confidence sets

In the paper, a sequential confidence set based on an estimation process of a multivariate parameter is constructed. Under the assumption that the estimation process scaled by an increasing positive process has an asymptotic distribution it is proved that the sequential confidence set is asymptotically consistent and asymptotic- ally efficient. The results are applied to the sequential confidence sets based on maximum likelihood estimators of a multivariate parameter in the iid case and in the exponential class of processes.