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The multiterminal theory of statistical inference deals with the problem of estimating or testing the correlation of letters generated from two (or many) correlated information sources under the restriction of a certain transmission rate for each source. A typical example is two binary sources with joint probability p(x, y) where the correlation of x and y is to be tested or estimated. Given n iid observations xn = x1 ...xn and yn=y1 ...yn, only k = rn (0 <; r <; 1) bits each can be transmitted to a common destination. What is the optimal data compression for statistical inference? A simple idea is to send the first k letters of xn and yn. A simpler problem is the helper case where the optimal data compression of xn is searched for under the condition that all of yn are transmitted. It is a long standing problem to determine if there is a better data compression scheme than this simple scheme of sending first k letters. The present paper searches for the optimal data compression under the framework of linear-threshold encoding and shows that there is a better data compression scheme depending on the value of correlation. To this end, we evaluate the Fisher information in the class of linear-threshold compression schemes. It is also proved that the simple scheme is optimal when x and y are independent or their correlation is not too large.