aggregate.hac {HAC}

Aggregation of variables

Description

aggregate tests, whether the absolute difference of the parameters of two subsequent nodes is smaller than a constant, i.e. \vert \theta_{2} - \theta_{1} \vert < \epsilon, where \theta_{i} denotes the dependency parameter with \theta_{2} < \theta_{1}, \epsilon \geq 0. If the absolute difference is smaller than the constant, the variables of the nodes are aggregated in a single node with new dependency parameter, e.g. \theta_{new} = (\theta_{1} + \theta_{2})/2. This procedure is applied to all consecutive nodes of the HAC x.

Usage

## S3 method for class 'hac'
aggregate(x, epsilon = 0, method = "mean", ...)

Arguments

x

an object of the class hac.

epsilon

scalar \geq 0.

method

determines, whether the new parameter is the "mean", "min" or "max" of the fused parameters.

...

further arguments passed to or from other methods.

Value

an object of the class hac.

See Also

hac

Examples

# Example 1:
# an object of the class hac is constructed, whose parameters are close
copula = hac(type = 1, tree = list("X1", list("X2", "X3", 2.05), 2))

# the function aggregate returns a simple Archimedean copula

copula_ag = aggregate(copula, epsilon = 0.1)
tree2str(copula_ag) # [1] "(X1.X2.X3)_{2.02}"

# the structure does not change for a smaller epsilon

copula_ag = aggregate(copula, epsilon = 0.01)
tree2str(copula_ag) # [1] "((X2.X3)_{2.05}.X1)_{2}"

# Example 2:
# consider the binary tree

Object = hac.full(type = 1, y = c("X1", "X2", "X3", "X4", "X5"), 
theta = c(1.01, 1.02, 2, 2.01))

tree2str(Object) # [1] "((((X5.X4)_{2.01}.X3)_{2}.X2)_{1.02}.X1)_{1.01}"

# applying aggregate.hac with epsilon = 0.02 leads to

Object_ag = aggregate(Object, 0.02)
tree2str(Object_ag) # [1] "((X3.X5.X4)_{2}.X1.X2)_{1.02}"