Abstract: This paper is focused on
the problem of comparison of experiments in the framework of DeGroot [5], Sinha
[15] and Stepniak [16]. We start with a family of bivariate normal populations
with arbitrarily specified means and variances and with different forms of the
correlation parameter and
examine the applicability of the concept of ‘sufficiency’ of one experiment
for another. We present a host of diverse results, exploiting this notion and
also using the expressions for Fisher information of the parameter “rho”.
Further, we extend to a family of trivariate normal populations with arbitrarily
specified means and variances with different forms of the equal/different
pair-wise correlation parameter and
examine the applicability of the concept of ‘sufficiency’ of one experiment
for another.
Keywords and phrases: bivariate/trivariate normal populations, Fisher information, sufficiency.
