On distributions admitting a sufficient statistic

Let x be a varate taking on values, determined by chance, on the axis of reals, R; and let the frequency function/(i, , 0,, x) be known, but involve v parameters (Si, , 0") which are unknown, but are confined to a known region 2 of real '-space.That is, we are assuming that if v values of (i, , S,) are given,A problem of practical importance is the statistical estimation of the parameters (i, , 0"): Let the result of n independent observations of x made on the assumption that (i, , 0") is fixed yield the numbers Xi, , xn,-the "sample" ; assuming nothing known a priori concerning the position of (i, , ") in fl, so that Bayes' formula is inapplicable, how can the sample Xi, ,xn be used to secure information regarding (0i, , 0,) ?According to R. A. Fisherf this problem is to be solved by finding v functions of n arguments, ,(xi, , xn) (J = 1, , v), such that when the arguments are replaced by the values in the sample, the resulting values are the appropriate values of ,.The question of how appropriateness is to be determined has its roots deep in the foundations of the subject, and will not be considered here.The function ij = l, ,v) exist, a question arises immediately which, stated intuitively, runs as follows : does the position of the single point (piixi, , xn), , v?Or is "relevant information" lost when Xi, , xn are discarded and only the numbers