CompleteRcvx: Complete a Partially Specified Correlation Matrix by Convex Optimization

Description

This function completes a partially specified correlation matrix by the method of convex optimization. The completed matrix will maximize the log(det(R)) over the space of PSD R matrices.

Usage

CompleteRcvx(Rna, Check_Convexity = TRUE, PRINT = TRUE)

Value

The CompleteCvxR function returns the following objects.

R (matrix) A PSD completed correlation matrix.
converged: (Logical) a logical that indicates the convergence status of the optimization.
max_delta The maximum absolute difference between the known elements in the partially specified R matrix and the estimated matrix.
convergence_status (list) A list containing additional information about the convergence status of the solution.

Arguments

Rna: (matrix) An n x n incomplete correlation matrix. Missing entries must be specified by NA values.
Check_Convexity: (logical) If Check_Convexity= FALSE the program will not check the convexity of the objective function. Since the convexity of the R completion problem is known to be true, setting this argument to FALSE can decrease computation time.
PRINT: (logical) If PRINT = TRUE then the program will print the convergence status of the final solution.

Author

Niels G. Waller

References

Georgescu, D. I., Higham, N. J., and Peters, G. W. (2018). Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance. Royal Society Open Science, 5(3), 172348.

Olvera Astivia, O. L. (2021). A Note on the general solution to completing partially specified correlation matrices. Measurement: Interdisciplinary Research and Perspectives, 19(2), 115--123.

Examples

Run this code

if (FALSE) {
  Rmiss <- matrix(
    c( 1,  .25, .6,  .55, .65,  0,  .4,   .6,  .2,  .3,
       .25, 1,    0,   0,   0,   0,  NA,   NA,  NA,  NA,
       .6,  0,   1,   .75, .75,  0,  NA,   NA,  NA,  NA,
       .55, 0,   .75, 1,   .5,   0,  NA,   NA,  NA,  NA,
       .65, 0,   .75,  .5, 1,    0,  NA,   NA,  NA,  NA,
       0,  0,    0,   0,   0,  1,   NA,   NA,  NA,  NA,
       .4, NA,   NA,  NA,  NA,  NA, 1,   .25, .25,  .5,
       .6, NA,   NA,  NA,  NA,  NA, .25,  1,  .25,  0,
       .2, NA,   NA,  NA,  NA,  NA, .25,  .25, 1,   0,
       .3, NA,   NA,  NA,  NA,  NA, .5,    0,   0,  1), 10,10)

  out <- CompleteRcvx(Rna = Rmiss,
                      Check_Convexity = FALSE,
                      PRINT = FALSE)

  round(out$R, 3)
}

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