estimate.gridCopula {GRIDCOPULA}

Estimates the parameters of a grid type copula

Description

This function estimates grid type copulas by one of the following methods: maximum likelihood or least squares (See reference).

Usage

estimate.gridCopula(
  X = NULL,
  U = NULL,
  k = NULL,
  m = NULL,
  method = "ml",
  D.ini = NULL,
  criterion = "AIC"
)

Arguments

X

a matrix of size nx2 with the observed values in any domain, optional if U is provided.

U

a matrix of size nx2 with the observed values in the copula domain, optional if X is provided.

k

a positive integer indicating the number of subintervals for the U_2 variable.

m

a positive integer indicating the number of subintervals for the U_1 variable.

method

the selected method for estimation, can be least squares "ls" or maximum likelihood "ml". By default "ml".

D.ini

an optional matrix with initial density values for the estimation through maximum likelihood.

criterion

If the values of k and m are not specified, they will be obtained by the "AIC" or "BIC" criteria, by default "AIC".

Value

Returns a list with a matrix with the density over the grid, a matrix with the quantity of data over the grid, the number of subintervals for the U_2 variable, the number of subintervals for the U_1 variable, a matrix with the values of u_1 and u_2 in the copula domain and a matrix with the original values X.

References

Pfeifer, D., Strassburger, D., & Philipps, J. (2020). Modelling and simulation of dependence structures in nonlife insurance with Bernstein copulas. arXiv. Retrieved from https://arxiv.org/abs/2010.15709

Examples

# Generating simulated data with a transformation to the copula domain
n <- 500
x <- rgamma(n,4,1/2)
e <- rnorm(n,0,.3)
y <- sin(x+e)
Fx <- ecdf(x)
Fy <- ecdf(y)
u <- Fx(x)
v <- Fy(y)
df <- cbind(u,v)
copula.grid <- estimate.gridCopula(U = df, k = 5, m = 4 , method = "ml")
print(copula.grid$Density)

# Using the Iris dataset, transformation is not mandatory
copula.grid <- estimate.gridCopula(X = iris[,1:2], k = 3, m = 7 , method = "ml")
print(copula.grid$Density)