CompleteRdev {fungible}

Complete a Partially Specified Correlation Matrix by the Method of Differential Evolution

Description

This function completes a partially specified correlation matrix by the method of differential evolution.

Usage

CompleteRdev(
  Rna,
  NMatrices = 1,
  MaxDet = FALSE,
  MaxIter = 200,
  delta = 1e-08,
  PRINT = FALSE,
  Seed = NULL
)

Arguments

Rna

(matrix) An n x n incomplete correlation matrix. Missing entries must be specified by NA values.

NMatrices

(integer) CompleteRDEV will complete NMatrices correlation matrices.

MaxDet

(logical) If MaxDet = TRUE then the correlation matrix will be completed with entries that maximize the determinant of R.

MaxIter

(integer) The maximum number of iterations (i.e., generations) allowed. Default MaxIter = 200.

delta

(numeric > 0) A number that controls the convergence accuracy of the differential evolution algorithm. Default delta = 1E-8.

PRINT

(logical) When PRINT = TRUE the algorithm convergence status is printed. Default PRINT = FALSE.

Seed

(integer) Initial random number seed. Default (Seed = NULL).

Value

CompleteRdev returns the following objects:

• R (matrix) A PSD completed correlation matrix.

• converged: (logical) a logical that indicates the convergence status of the optimizaton.

• iter (integer) The number of cycles needed to reach converged solution.

Author(s)

Niels G. Waller

References

Ardia, D., Boudt, K., Carl, P., Mullen, K.M., Peterson, B.G. (2011) Differential Evolution with DEoptim. An Application to Non-Convex Portfolio Optimization. URL The R Journal, 3(1), 27-34. URL https://journal.r-project.org/archive/2011-1/RJournal_2011-1_Ardia~et~al.pdf.

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.

Mauro, R. (1990). Understanding L.O.V.E. (left out variables error): a method for estimating the effects of omitted variables. Psychological Bulletin, 108(2), 314-329.

Mishra, S. K. (2007). Completing correlation matrices of arbitrary order by differential evolution method of global optimization: a Fortran program. Available at SSRN 968373.

Mullen, K.M, Ardia, D., Gil, D., Windover, D., Cline, J. (2011). DEoptim: An R Package for Global Optimization by Differential Evolution. Journal of Statistical Software, 40(6), 1-26. URL http://www.jstatsoft.org/v40/i06/.

Price, K.V., Storn, R.M., Lampinen J.A. (2005) Differential Evolution - A Practical Approach to Global Optimization. Berlin Heidelberg: Springer-Verlag. ISBN 3540209506.

Zhang, J. and Sanderson, A. (2009) Adaptive Differential Evolution Springer-Verlag. ISBN 978-3-642-01526-7

Examples

## Example 1: Generate random 4 x 4 Correlation matrices.
  Rmiss <- matrix(NA, nrow = 4, ncol = 4)
  diag(Rmiss) <- 1

  out <- CompleteRdev(Rna = Rmiss,
                      NMatrices = 4,
                      PRINT = TRUE,
                      Seed = 1)

  print( round( out$R[[1]] , 3) )

## Not run: 
# Example 2: Complete a partially specified R matrix.
# Example from Georgescu, D. I., Higham, N. J., and
#              Peters, G. W.  (2018).

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)

# Complete Rmiss with values that maximize
# the matrix determinant (this is the MLE solution)
 set.seed(123)
 out <- CompleteRdev(Rna = Rmiss,
                     MaxDet = TRUE,
                     MaxIter = 1000,
                     delta = 1E-8,
                     PRINT = FALSE)

cat("\nConverged = ", out$converged,"\n")
print( round(out$R, 3))
print( det(out$R))
print( eigen(out$R)$values, digits = 5)

## End(Not run)