数学中国w, madio,net The Most Expensive is Not the Best 159 where E is the transpose of E and r,=>=, wS ( k)is the relating de- gree. The vector R=(u ., r,.)contains the final scores of the countries healthcare systems. The larger r the better the system How to Determine the Weights Wewe want to determine the weight vector in a credible way. We use the principle of minimum loss I Wang et aL. 2000. Because our metrics ul, evaluate information from different aspects, combining all the metrics in a informatics We should maximize conservation of information. So we choose the most classical method: We calculate variance to represent information; the larger the variance, the more information. In the final scored=w u, we should choose the best weight w to make the variance of d reach the maximum: D(d)=w D(uw where D(d) is the variance matrix of d. when ww=l, D(d)achieves it maximum We use the method of Lagrange multipliers. Suppose that =2D(u)u-2)=0 入 which reduces to D(uw=Aw, 1 So Ais aneigenvalue of D(u with eigenvector w when ww=l, to make the maximum eigenvahtw= A reach the maximum, we should take Aas D() lue of D (u) In the real calculation, we do not know D(u), so we use the variance matrix D(u)=ou)of the sample(cin,., Cn)of u, to represent it, where (x-x)(数学中国 www.madio.net