相关系数与协方差间的转换

首先，相关系数和协方差间的数学关系为：



其次，上述数学表达式在sas/iml中的算法表达如下，R为相关系数矩阵，S为对角阵, COV协方差矩阵



其中:



最后，上代码：

***** Program 4.10 PROC IML ***********;
***** Converting a correlation matrix to covariance matrix, and vice versa;
***** Example data from Table 4.4 ;
****** Part I: Converting correlation matrix to covariance matrix;
PROC IML;

*** define the correlation matrix;
R={1.00 0.70 0.20,
0.70 1.00 0.40,
0.20 0.40 1.00};

*** define the diagonal matrix with standard deviations on the diagonal;
S={15 0 0,
0 10 0,
0 0 1};

*** obtain the covariance matrix;
COV=S*R*S;

*** print the covariance matrix;
PRINT COV;
RUN;

***** Part II: Converting covariance matrix to correlation matrix;
PROC IML;

*** define the covariance matrix;
COV={225 105 3,
105 100 4,
3   4 1};

*** obtain the matrix with standard deviations on the diagonal;
S=SQRT(DIAG(COV));

*** the inverse of S matrix;
S_INV=INV(S);

*** obtain correlation matrix;
R=S_INV*COV*S_INV;

** print out the three matrices;
PRINT COV S R;
RUN;

FROM 《SAS for Monte Carlo Studies》，P96-97