A Note on the attainment of the cramér-rao bound in the sequential case

Abstract

Under some assumptions, Ghosh (1987) has shown that the Cramér-Rao bound is attained for some strictly sequential procedure if and only if the observations follow the Bernoulli distribution. An extension of this result to the multivariate case via the arguments of Stefanov (1985) is presented. Furthermore, by imposing additional assumptions, we try to find an "analogue" of the above result of Ghosh in the multivariate case. In the latter case the role of the Bernoulli distribution is performed by the multivariate Bernoulli distribution.

Keywords:

• Exponential families
• sequential estimation
• Cramér-Rao bound