matrix_estimation {NetworkRiskMeasures}

Matrix Estimation

Description

Methods for estimating matrix entries from the marginals (row and column sums).

There are currently two methods implemented: Maximum Entropy (Upper 2004) and Minimum Density (Anand et al. 2015).

You may use the matrix_estimation() function, setting the desired method. Or you may use directly the max_ent() function for maximum entropy estimation or the min_dens() function for minimum density estimation.

Usage

matrix_estimation(
  rowsums,
  colsums,
  method = c("me", "md"),
  ...,
  max.it = 1e+05,
  abs.tol = 0.001,
  verbose = TRUE
)

max_ent(rowsums, colsums, max.it = 1e+05, abs.tol = 0.001, verbose = TRUE)

min_dens(
  rowsums,
  colsums,
  c = 1,
  lambda = 1,
  k = 100,
  alpha = 1/sum(rowsums),
  delta = 1/sum(rowsums),
  theta = 1,
  remove.prob = 0.01,
  max.it = 1e+05,
  abs.tol = 0.001,
  verbose = TRUE
)

Arguments

rowsums

a numeric vector with the row sums.

colsums

a numeric vector with the column sums.

method

the matrix estimation method. Choose "me" for maximum entropy or "md" for minimum density.

...

further arguments passed to or from other methods.

max.it

the maximum number of iterations.

abs.tol

the desired accuracy.

verbose

gives verbose output. Default is TRUE.

c

the 'cost' an extra link for the minimum density estimation. See Anand et al. (2015).

lambda

you should use lamda together with k. For the first k rounds of the algorithm, the function will allocate a fraction lambda of the total, thus obtaining a "low density" solution, instead of a "minimum density" solution. See Anand et al. (2015).

k

you should use lamda together with k. For the first k rounds of the algorithm, the function will allocate a fraction lambda of the total, thus obtaining a "low density" solution, instead of a "minimum density" solution. See Anand et al. (2015).

alpha

weights for the row sums deviations. See Anand et al. (2015).

delta

weights for the column sums deviations. See Anand et al. (2015).

theta

scaling parameter. Emphasizes the weight placed on finding solutions with similar characteristics to the prior matrix. See Anand et al. (2015).

remove.prob

probability to randomly remove a link during the algorithm. See Anand et al. (2015).

Value

The functions return the estimated matrix.

References

Upper, C. and A. Worm (2004). Estimating bilateral exposures in the German interbank market: Is there a danger of contagion? European Economic Review 48, 827-849.

Anand, K., Craig, B. and G. von Peter (2015). Filling in the blanks: network structure and interbank contagion. Quantitative Finance 15:4, 625-636.

Examples

# Example from Anand, Craig and Von Peter (2015, p.628)

# Liabilities
L <- c(a = 4, b = 5, c = 5, d = 0, e = 0, f = 2, g = 4)

# Assets
A <- c(a = 7, b = 5, c = 3, d = 1, e = 3, f = 0, g = 1)

# Maximum Entropy
ME <- matrix_estimation(A, L, method = "me")
ME <- round(ME, 2)

# Minimum Density
set.seed(192)
MD <- matrix_estimation(A, L, method = "md")