Sequential estimation continues observations until the observed sample satisfies a prescribed criterion. Its properties are superior on the average to those of nonsequential estimation in which the number of observations is fixed a priori. A higher-order asymptotic theory of sequential estimation is given in the framework of geometry of multidimensional curved exponential families. This gives a design principle of the second-order efficient sequential estimation procedure. It is also shown that a sequential estimation can be designed to have a covariance stabilizing effect at the same time.
Ichi Okamoto. Shun-Ichi Amari. Kei Takeuchi. "Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach." Ann. Statist. 19 (2) 961 - 981, June, 1991. https://doi.org/10.1214/aos/1176348131