  We present a geometrical method for analyzing sequential estimating
procedures. It is based on the design principle of the second-order efficient
sequential estimation provided in Okamoto, Amari and Takeuchi (1991). By
introducing a dual conformal curvature quantity, we clarify the conditions for
the covariance minimization of sequential estimators. These conditions are
further elabolated for the multidimensional curved exponential family. The
theoretical results are then numerically examined by using typical statistical
models, von Mises-Fisher and hyperboloid models.
